NCCER Module 2
Of the numbers listed, which one has the lowest value?
0.0001
To properly align the shaft of a base-mounted pump to the shaft of its driver (usually an electric motor), very thin shims must be placed under the mounting feet. You must report the total thickness of the shims placed under each foot. Shims are provided in precise thicknesses, measured in thousandths of an inch. In this case, three shims were placed under one foot. One shim is marked 0.030", the second is marked as 0.015", and the third is marked as 0.007". What is the total thickness of the three shims? Your answer should be to the nearest thousandth of an inch.
0.052
You pay sales tax on your purchases at the rate of 0.07. What fraction of your money is this? Remember to reduce your fraction to its lowest terms.
0.07 is equal to 7/100
Ivan has cut 19 pieces of reinforcing bar (rebar) that are each 1.14 meters long. What is the total length of the rebar used for the project? Your answer should be to the nearest hundredth of a meter.
21.66
You have a barrel of ethylene glycol that will be used as antifreeze in a heating water system. The barrel is 7/8 full, and you need to provide 3/5 of it to another worker. What fraction of a full barrel do you need to give the other worker? Your answer should be stated as a fraction reduced to its lowest terms.
21/40
An estimator is preparing a bid for a home remodeling project. She has determined that the new garage needs 324 feet of 2x10 lumber; the new rec room requires 430 feet; and the new upstairs bonus room needs 283 feet. How many feet of 2x10 lumber will be needed?
1,037 feet
One yard of gravel has been delivered to a jobsite and you have been instructed to spread ½ of it in front of the temporary steps to a building and 1/3 of it in front of the door to the jobsite trailer. How much gravel will be left over? Your answer should be in the form of a fraction reduced to its lowest terms.
1/6
Four boards must be replaced, each ¾ of a foot long. How long must a board be to cut these four pieces? Your answer should be a whole number.
3 feet
A chemical injection system tank is 3/4 full and pumps out at a rate of 1/8 of a tank per week. You won't be back for five weeks. How much will be left in the tank when you return? Your answer should be in the form of a fraction reduced to its lowest terms.
1/8
You have 3/4 of a tank of fuel to power a compressor that uses 1/8 tank per hour. If you work 3 hours in the morning (using 3/8 of a tank) and 2 hours in the afternoon (using 2/8 of a tank), how much of the tank remains? Your answer should be in the form of a fraction reduced to its lowest terms.
1/8
A ¾-ton pallet of tile has been delivered to the job site. It is to be used for 6 equal restrooms in a commercial building. What fraction of this ¾-ton of tile will be set aside for each restroom? Your answer should be reduced to its lowest terms.
1/8 ton of tile
On Thursday, you were told that you would be driving to a job 39½ miles away. Since your odometer displays mileage in decimal form, how will 39½ miles appear on it?
39.5 miles
A length of pipe is 5.5 meters long. How many 1.2 meter lengths op pipe can be cut from that one length of pipe?
4
You measure the length of a short pipe nipple that must be cut and arrive at the fraction 28/32 inch. Reduce this fraction to its lowest terms.
7/8 inch
A 1200-gallon tank is 62% full when it contains _____ gallons.
744
There are three homes being built, each with an identical deck on the back. Each deck is comprised of two separate areas. One area is 112.5 square feet, while the other is 136.4 square feet. What is the total square footage of the decks for all three homes? Your answer should be to the nearest tenth of a square foot.
746.7 sq ft
In trying to decide if you have enough nails to complete a job, you estimate you have about 80 percent of a box remaining. If you started with a 15-pound box of nails, how many pounds of nails remain? State your answer as a whole number.
12 lbs of nails left
A job site manager has been given permission to hire student workers for a single week to do preparatory work on the site. He's been allocated $6,000 for this purpose. Assume that each student is paid $12 per hour and works a standard 40-hour week. How many students can he hire? The result should be a whole number, since you cannot hire part of a person. If there is any remainder, it should be ignored as a result.
12 students
While preparing to paint columns on a small office building, you realize you have 7/8 of a gallon of paint remaining. Each column requires 1/16 of a gallon of paint. How many columns will you be able to paint? Your answer should be stated as a whole or mixed number reduced to its lowest terms.
14
A section of pipe is needed to complete a compressed-air line. David says he has 2/3 of a pipe length left, while Don says he has 11/16 of a length left. Which person has the longest section left?
Don
The instructions for mixing cement call for 1 gallon of water to be used with one sack of cement. Will 2/7 of a partial sack (Sack A) require more or less water than ¼ of a partial sack (Sack B)? In other words, which sack of cement is the largest, Sack A or Sack B?
Sack A
A contractor places an order with a building supply company for three exterior doors to be installed in a new home. The front door costs $635, the door to the garage costs $355, and the sliding door to the deck costs $1,232. What is the total amount of the order?
$2,222
Each laborer earns $12.00 per hour. Alfredo's weekly time card shows 28 hours worked, Bob's card shows 40 hours of work, and Jane's card shows 38 hours of work. Excluding any deductions, how much money must be set aside to pay these three laborers?
$1,272
Profit is the amount of money that remains after all expenses of a project have been paid. The year has just ended, and Ajax Construction's owner is anxious to find out if the company had a profitable year. The company was awarded five contracts totaling $7,435,000. The costs associated with each project were: Project 1: $1,245,000 Project 2: $985,689 Project 3: $1,723,000 Project 4: $2,567,054 Project 5: $633,768 How much profit did the company earn?
$280,489
At the end of a construction project, the project manager is totaling up the cost of building materials used on the job. He arrives at the following costs: Lumber: $15,432 Piping: $4,522 Concrete: $3,445 Drywall: $6,489 Paint: $882 How much was spent for materials on this project?
$30,770
Profit is the amount of money that remains after all expenses of a project have been paid. Acme Construction has just completed the construction of a building, and Fred Jones, the project manager, is doing the final accounting. Acme bid $232,500 for the project and was awarded a contract for that amount. The cost of construction, including labor, building materials, and other expenses such as equipment rental was $198,468. What was the profit on this project?
$34,032
You are preparing for a job and need a load of lumber. One store offers to ship the order for $500.00. Another offers you the same deal at 8 percent less. How much money will you save if you accept the second offer?
$40
A painter is buying 5-gallon containers of white paint for a job at a large apartment complex. His local supplier is having a sale, with each container costing $43. If he buys 12 containers, how much will he pay before sales tax is added?
$516
You must mix two dry ingredients at a ratio of 1 gram of Ingredient A to 4 grams of Ingredient B. Ingredient B however, is packaged in ounces. You know that one ounce equals 28.35 grams. How many ounces of Ingredient B are required for each gram of Ingredient A in the mixture? Round your answer to the nearest hundredth of an ounce.
0.14
While installing a window in an older home, you find that the measurements are not square and will need to shim one side. You find a packet of shims that have 0.25 inch marked on the outside of the wrapper. What fraction of an inch is 0.25, reduced to its lowest terms?
0.25 is equal to the fraction 1/4
A small job is going to require a 60-pound bag of cement mix. It states on the bag that the resulting concrete will consist of 11 percent cement, 41 percent gravel, 26 percent sand, and 16 percent water. What is the portion of the sand in the mix, stated in decimal form? Your answer should be to the nearest hundredth.
0.26
The decimal equivalent of 2/5 is _____.
0.40
A 2.5-meter piece of framing lumber has been used to cut a piece 1.65 meters long. How much of the original piece of lumber remains, in meters? Your answer should be to the nearest hundredth of a meter.
0.85
One gallon of primer is required to coat a hallway. You have three partially full gallon cans. One is 1/4 full, another is 1/2 full, and the third is 1/3 full. How much paint do you have? Your answer should be in the form of a whole or mixed number.
1 1/12 gal
A truck delivering material to a construction site must make several stops. Each stop is 1/2-mile apart. The total distance between the stops totals 3/2 miles. Change this fraction to a mixed number, reduced to its lowest terms.
1 1/2 miles
You are installing 250 feet of PVC conduit. Each 100-foot section takes 1/2 can of PVC cement, and each 50-ft section takes 1/4 can. How much cement do you need? Your answer should be in the form of a mixed number, with any remaining fraction in its lowest terms.
1 1/4
A chimney is located 5 feet away from the vent connection on a furnace. The furnace manufacturer states that the vent connector must have at least 1/4′′ per foot of upward slope per foot of horizontal distance between the furnace and the chimney. In the distance between the furnace and the vent, what is the minimum change in elevation from where the vent connector pipe is attached to the furnace to where it connects to the chimney that is required?
1 1/4"
Concrete block walls are often filled with an insulating material such as vermiculite. Each block has square cells that are filled, and each block holds 256 cubic inches of vermiculite. The vermiculite must be ordered in cubic meters. You know that one cubic meter is equal to 61,023.7 cubic inches. If there are 300 blocks to fill in a wall, how much vermiculite, in cubic meters, will be required? Round your answer to the nearest tenth of a cubic meter.
1.3 cubic meters
A floor pattern uses small pieces of flooring to create a visual display. You want to cut the 2/3-foot of wood you have into 8 small, equal sections. How long will each section be? Your answer should be a fractional portion of one foot, reduced to its lowest terms.
1/12 of a foot
You are part of a team of seven carpenters who are sharing a box of finish nails. There is ½ pound of nails in the container. How much of the box of nails will each carpenter receive? Your answer should be stated as a fractional portion of a pound of nails, reduced to its lowest terms.
1/14 lbs of nails
3/4 of a pound of nails are in a container. You use 1/3 of the nails. How much of the nails did youuse? Your answer should be stated as a fraction reduced to its lowest terms.
1/4
You just dropped off a company truck that you are required to return with the gas tank at a minimum of 1/4 full, but you forgot to check the gauge until you passed by the gas station. You used about 1/2 tank getting to and from one job site, and then made a side trip to another job site that used up another 1/4 tank. If you started with a full tank, how much will be left? Your answer should be in the form of a fraction reduced to its lowest terms.
1/4
The dimensions around the perimeter of an irregular shaped concrete form are 11 5/16′′, 36 1/2′′, 44 1/8′′ and 16 1/4′′. What is the distance around the perimeter of this form?
108 3/16"
You must add powdered dye to water to make a water-based stain. For the amount of stain you need to make, 4 ounces of dye is required. The dye is sold in packages weighed in milligrams. You know that one ounce is equal to 28,350 milligrams. How many milligrams of the dye are required to make the stain? This answer will be a whole number.
113,400 mg
After a very intense, multiday storm, your 1,375 square-foot basement has flooded to a depth of 18 inches. That's equivalent to about 15,425 gallons of water! You haven't been able to get a water removal company to come since they are overloaded with jobs. Your boss suggests that you borrow the company's submersible utility pump and do the job yourself. It can pump 1,200 gallons of water per hour. To the nearest hour, how long will it take to drain your basement?
13 hours
A worksite cleanup crew of 23 has had to work overtime to finish a job by a contract date. If each member of the crew worked 63 hours during the week, how many total hours did the crew put in?
1449 hours
Gene is laying out the site for a building that will serve as a new distribution center. He determines that he will need to have 290 cubic yards of soil to fill depressions on the site in order to bring it up to the desired grade. The dump truck is of European manufacture, and all he knows is that its capacity is 15 cubic meters. You know that a cubic yard is the same as 0.764 cubic meters. How many trips will the truck have to make to haul the required soil to the site? Your answer should be rounded up to a whole number, since the truck cannot make part of a trip.
15 trips
Frame carpenters typically work with measurements as small as 1/16 inch. Trim carpenters and cabinetmakers may work with measurements as small as 1/64 inch. Find the lowest common denominator for the fractions 6/16 and 12/64. Your answer should be a whole number, representing the lowest common denominator.
16
You have six 4-foot lengths of lumber, and you need 2/3 of them for a project. How many feet of lumber are you using for the project? Your answer should be a whole or mixed number.
16 feet
A piece of equipment that must be lifted to the roof of a structure has arrived. The maximum capacity of the crane under the circumstances, based on the lift plan, is 19,800 kilograms. However, the specifications for the piece of equipment, including its weight, are in imperial units. The shipping documents indicate that it weighs 37,845 pounds. What is the weight of the equipment in kilograms? Round your answer to the nearest whole number.
17,163 kg
A plumbing contractor bid the rough-in work for a new three story office building based an estimate of 850 hours of a journey-level plumber's time on the job. After the job was in progress, the contractor determined that the first floor required 342 hours and the second floor required 329 hours. How many labor hours are left in estimate to complete the third floor?
179 hours
An instrument technician uses an infrared (noncontact) thermometer to measure the temperature of a running motor. According to the motor's manual, the operating temperature should not exceed 220°F. Although the thermometer can display either Fahrenheit or Celsius, the button that switches scales is unfortunately broken. The thermometer shows a temperature of 83°C. To the nearest whole degree, what is the equivalent Fahrenheit value?
181°F
The building under construction requires 16 concrete pilings to serve as the foundation. The construction crew has created the forms for the pilings and is ready to pour the concrete into the forms. According to the drawings, each form will require 10 cubic meters of concrete. The concrete at this site must be ordered by the cubic yard. One cubic meter is equal to 1.308 cubic yards. How many cubic yards of concrete will the crew have to order? Round your answer up to the nearest whole number, since orders must be placed as whole yards.
210 cubic yards
As air is moved through a duct by a fan, friction between the air molecules and the sides of the duct creates a resistance to movement. Friction loss charts are available to determine the friction loss for a given quantity of air passing through a given size of duct, per 100 feet of duct. You know that a section of exhaust duct is 64 meters long, but you cannot determine the friction loss unless the duct length is in feet. You know that one meter is equal to 3.28 feet. How long is the 64-meter section of duct in feet? Round your answer to a whole number.
210 ft
After driving to your long-distance jobsite, you have emptied your 14-gallon tank of gasoline. Your trip odometer says you've put 313.6 miles on your vehicle. How many miles to the gallon did you get? Your answer should be in the form of a fraction or mixed number reduced to its lowest terms.
22 2/5 miles per gallon
Asphalt roofing shingles are typically sold by the square, with a square covering 100 square feet. A contractor must shingle a roof that measures 65.5′ × 35′. How many squares will be required to cover this roof?
23
You have added together the lengths of several wood shims to be cut. Adding them together resulted in a total of 61/16 inches. Convert this improper fraction to a mixed number.
3 13/16 inches
A total of 42 gallons of a glycol solution needs to be added to a heating water loop to ensure the water does not freeze if there is a heating equipment failure. The glycol solution comes in 1.75-gallon cans. How many cans will be needed? Your answer should be a whole number.
24
You're working for a telecom cable installation company that's running the network wiring for a large office building. Your boss notices that there is a partial box of Category 5e cable left over from the job. It contains 365 feet of cable. He suggests that you make it into 15-foot patch cables. How many cables will you be able to make? Your answer should be rounded down to the nearest whole number, since a cable shorter than 15 feet is not desired.
24 cables
You need to return 0.25 ton of sand left over from a job. Express which part of a ton you will return as a whole-number percentage.
25
Troy must keep track of the amount of refrigerant he uses from a 50-pound cylinder to ensure that accurate records are kept. He used 13 pounds on a system for Ms. Jones and 9 pounds on a system for a commercial client. How many pounds should he have left in the cylinder?
28 lbs
A welding drawing shows that the weld-root reinforcement cannot exceed 1/8" in thickness. Your weld measurement tools are metric, so this value needs to be converted to millimeters. You know that one inch equals 2.54 centimeters. What is the maximum weld-root reinforcement allowed in millimeters? Round your answer to the nearest tenth of a millimeter.
3.2 mm
When 0.60 is converted to a fraction, it becomes _____.
3/5
You're spending the summer working for a drywall contractor. One day he sends you into the storeroom to see how many drywall screws are left. There are 8 boxes on the shelf, each holding 5 pounds of screws. Your boss mentions that there are about 83 screws per pound. About how many screws are there total?
3320 drywall screws
An insulator is installing fiberglass insulation in exterior walls that total up to 1,623 square feet after windows and doors are deducted. Each roll can insulate 49 square feet. There are 28 rolls on hand. Will this amount be sufficient? If not, how many total rolls are needed? If necessary, round your answer up to the nearest whole number, since you cannot buy part of a roll of insulation.
34 rolls
You are laying a subfloor and need 1/8 pound of nails for each sheet of plywood. You have ½ pound of nails in the box. How many sheets can you nail down before having to restock your nails? Ensure your answer is converted to a whole or mixed number reduced to its lowest terms.
4 sheets
You have a one-liter can of paint thinner, and use 1/3 of it to clean brushes and 2/5 of it to reduce the viscosity of the paint in a sprayer system. What part of the liter will be left? Your answer should be in the form of a fraction reduced to its lowest terms.
4/15
The amount of soil moved into an area over the course of a workday must be documented in metric tons. The scale that weighs the trucks documents the net weight in pounds. You know that a metric ton is equal to roughly 2,205 pounds. If the scales operator reports that 93,400 pounds of soil moved across the scale in a workday, how many metric tons will you record in your report? Round your answer to the nearest tenth of a metric ton.
42.4 tons
An electrician's apprentice has been sent to a supply center to pick up 17 rolls of flexible 3/4′′ conduit for an upcoming job. Each roll contains 25 feet of conduit. How many feet of conduit is he taking back to the job site?
425 ft
A set of civil construction plans shows a distance of 131 meters across the front of a piece of property. You need to convert this value to feet. You know that one foot equals approximately 0.305 meters. What is the distance in feet, to the nearest tenth of a foot?
429.5 feet
A project needs five filler panels of drywall, each of which must be 9/12 inches wide. The drywall mechanic determines that the total width of the drywall needed to cut out the five pieces is 95/2 inches. Change this value to a mixed number.
47.5 inches wide
Sally works as an estimator for G&J Electric. She has determined that 550 feet of electrical cable will be needed to wire a new house. Later, Sally is told that the homeowner has decide to cut back from a three-car garage to a two-car garage, which will eliminate two branch circuits, one of 23 feet and the other of 34 feet. How many feet of wire will be needed now?
493 feet
Brian is responsible for ordering cement for a construction project. He had just determined that the construction crew would need 540 cubic yards of cement when the building owner decided to shorten the driveway, eliminating the need for 44 cubic yards of cement. How much cement will Brian have to order now?
496 cubic yards
Seven 2 × 4s have been cut shorter, with the waste pieces measuring 3/4-inch each. Adding the lengths together results in the fraction 21/4 inches. Change this number to a mixed number.
5 1/4 inches
A set of plans shows that an opening in a bulkhead is needed for a section of pipe to pass through. The plans show metric values, but the only tape measure available is marked in inches. The pipe is shown as a size DN80 (a European pipe-sizing standard), and a chart indicates the outside diameter of DN80 pipe is 88 millimeters (mm). According to the plans, all openings must be 40 mm larger than the pipe. You know that 25.4 mm is equal to one inch. What is the diameter of the needed opening in inches? Round your answer to the nearest whole inch.
5 inches
A refrigeration unit requires 4.6 pounds of refrigerant. Using a metric scale, you determine that there are 2.3 kilograms of refrigerant remaining in the charging cylinder. You know that one kilogram is the same as 2.205 pounds. How many pounds of refrigerant are in the cylinder? Round your answer to the nearest tenth of a pound.
5.1 pounds
You are driving along and see that your tank is 5/8 full. The tank holds 14 gallons of gas. You need to fill up before a long drive. How much fuel should register on the gas pump when your car is full, assuming the gas gauge reading is precise? Your answer should be in decimal form to the nearest hundredth of a gallon.
5.25 gallons
You are mixing a textured additive into paint and each liter of paint requires 1/8 kilogram (kg) of additive. You need 1/2 liter of paint with 1/16 kg of additive for the trim, and 2 liters of paint with 1/4 kg of additive for the walls. How much additive will you require altogether? Your answer should be in the form of a fraction reduced to its lowest terms.
5/16 kg
A list of needed materials calls for one five-pound pack of deck screws. You have three leftover packs. Two of them are 1/4 full, and the third pack is 1/3 full. Expressed as a fraction, what part of a full 5-pound pack of nails do you have?
5/6
When 5/8 ÷ 3/4, the answer is ...
5/6
A flooring contractor is going to lay a vinyl tile floor in a rectangular room 27 feet × 19 feet. He knows that to find the number of square feet in a rectangle, it is necessary to multiply its length by its width. Each tile covers one square foot of floor. How many tiles will he need to cover the floor?
513 tiles
Asphalt roofing shingles are typically sold by the square, with a square covering 100 square feet. A contractor must shingle a roof that measures 65.5′×35′. As a rule of thumb, 2.5 pounds of roofing nails are required to install each square. How many pounds of roofing nails are required to complete this job?
57.5
The engine displacement of your plumbing service truck, which roughly represents the total active area of the eight cylinders and combustion chambers, is rated at 350 cubic inches. What is the engine's displacement in cubic centimeters, if one cubic inch is equal to 16.39 cubic centimeters? Your answer should be rounded to the nearest tenth of a cubic centimeter.
5736.5 cubic cm
How many 1 1/4′ by 4′ pieces can you cut from a 4′ × 8′ sheet of plywood?
6
To prepare for the alignment of numerous pumps, you need to have 50 pieces of 1/8-inch brass shim stock on hand. If you stack the 50 shims on top of each other, how tall would the stack be, shown as a whole or mixed number? (Hint: You must also reduce any fraction that might remain to its lowest terms.)
6 1/4 in
You've been assigned to paint the concrete floor of the instrumentation shop at your plant. The floor has an area of 1,445 square feet. Each can of epoxy floor paint is supposed to cover 275 square feet. How many cans will you need to paint the floor with a single coat? Your answer should be rounded up to a whole number, since you cannot buy part of a can of paint.
6 cans
A hydraulic fluid tank is 3/5 full. How would you express the amount of fluid in the tank as a whole-number percentage?
60 percent full
A project superintendent for Acme Construction is ready to order concrete for the foundation slab of the building to which he has been assigned. Looking at the drawings, he realizes that the concrete volume is specified as 50 cubic meters. He knows that Superior Concrete will want to know the volume in cubic yards. With the knowledge that there 1.308 cubic yards to one cubic meter, how many cubic yards of concrete should he order? Your answer should be to the nearest tenth of a cubic yard.
65.4 cubic yards
While replacing windows for an older building, you find one that measures 1¾ feet square. What is the distance around the window in feet? Your answer should be stated as a whole or mixed number reduced to its lowest terms.
7 ft
Full productivity is achieved when a crew pours and finishes 65 cubic yards of concrete in a day. The superintendent on the project has promised the crew a bonus if it can exceed its daily requirement by 125%. How much concrete in cubic yards, must the crew pour and finish toachieve this goal?
82 yards
Rounded to the nearest thousandth, the number 82.17420118 is _____.
82.174
You are lubricating several motors in the shop. One motor must be lubricated with 3/16 of an ounce of grease, and one larger motor must be lubricated with 3/8 of an ounce of grease. How many ounces of grease will you require? Your answer should be a fraction of an ounce, reduced to its lowest terms.
9/16 of an ounce
A warning placed in an installation manual for a piece of equipment indicates that the equipment must not be placed within 36 inches of flammable material. You need to know the value in centimeters (cm), and you know that one inch equals 2.54 cm. What is the allowable distance to flammable material in centimeters, to the nearest hundredth of a centimeter?
91.44
The estimator for a heating, ventilation, and air conditioning (HVAC) contractor estimated that the new hospital would require 5,840 feet of sheet metal ductwork. The order is too large for a single fabricator, so it was decided to split the order among four fabricators. Fabricator 1 received an order for 2,500 feet; Fabricator 2 obtained an order for 1,200 feet; and Fabricator 3 was awarded a contract for 1,150 feet. How many feet of ductwork would be required of Fabricator 4?
990 feet
Which of the following fractions is equivalent to 1/2?
All of the above (4/8, 32/64, 8/16)
Two 8-foot-long 2 × 4's are cut into sections of equal length. Board A is cut into 9 equal sections, of which 5 are used. Therefore, 5/9 of the board has been used; 4/9 of it remains. Board B is cut into 7 equal sections, of which 4 are used. That means 4/7 of the board has been used; 3/7 of it remains. Which has the longest remaining section, Board A or Board B?
Board A
A driver is given $600.00 in cash and told to pick up 130 sheets of sheetrock at $4.15 per sheet. He is also told to up pick extra pails of joint compound if he has enough cash left. Each pail of joint compound costs $29.50. Does the driver have enough cash left over to pick up 4 pails of joint compound?
No
The site material coordinator ordered (800) 2 × 4s for a project. She needs to reorder an equal amount when the current inventory gets down to the 30% level. The carpenters report that they have used about 450 of the studs to date. Is it time to reorder more studs?
No
An HVAC contractor must install ductwork in six identical homes in a small development. She has calculated that each home will require about 215 square feet of galvanized sheet metal to fabricate all the required ducts in each house. The shop supervisor has set aside 1400 square feet of sheet metal for the project. Has he set aside enough sheet metal to complete the job?
Yes
Metric rulers are typically divided into _____.
millimeters and centimeters