Measurement and Problem Solving (chapter 2)

Rules to determine significant numbers:

1. All nonzero digits are significant. 2. Interior zeros (zeros between two numbers) are significant. 3. Trailing zeros (zeros to the right of a nonzero number) that fall after a decimal point are significant. 4. Trailing zeros that fall before a decimal point are significant. 5. Leading zeros (zeros to the left of the first nonzero number) are not significant. They only serve to locate the decimal point. 6. Trailing zeros at the end of a number, but before an implied decimal point, are ambiguous and should be avoided by using scientific notation. (350 should be written as 3.5 x 10(2nd)

What sources do exact numbers originate from?

1. Exact counting of discrete objects. (5 atoms means 5.00000... atoms). 2. Defined quantities, such as a number of centimeters in 1 m. Because 100cm is defined as 1m, (100cm =1m means 100.00000...cm = 1.000000000...m) 3. Integral numbers that are part of an equation. Radius = diameter/2, the number 2 is exact and therefore has an unlimited number of significant numbers.

conversion factor

A factor used to convert between two separate units; a conversion factor is constructed from any two quantities known to be equivalent.

density (d)

A fundamental property of materials that relates mass and volume and differs from one substance to another. The units of density are those of mass divided by volume, most commonly expressed in g/cm(3 cubed), g/mL, or g/L.

Which is the most convenient unit to use to express the dimensions of a polio virus, which is about 2.8 x 10(-8th)m in diameter? a. Mm b. mm c. µm d. nm

d. nm

Express 16,342,000,000,000 in scientific notation.

1.6342 x 10(13th power)

The radius of a dust speck is 4.5 x 10(-3rd power)mm. What is the correct value of this number in decimal notation?

0.0045mm

Perform the calculation to the correct number of significant figures: 1.01 x 0.12 x 53.51 / 96 =

0.067556 = 0.068

1 US gallon (gal) = x liters (L)

1 gal = 3.785 L

SI prefix multipliers 1. tera- T 2. giga- G 3. mega- M 4. kilo- k 5. hecto- h 6. deca- da 7. deci- d 8. centi- c 9. milli- m 10. micro- µ 11. nano- n 12. pico- p 13. femto- f

1. trillion 10(12th) 2. billion 10(9th) 3. million 10(6th) 4. thousand 10(3rd) 5. hundred 10(2nd) 6. ten 10(1st) 7. tenth 10(-1st) 8. hundredth 10(-2nd) 9. thousandth 10(-3rd) 10. millionth 10(-6th) 11. billionth 10(-9th) 12. trillionth 10(12th) 13. quadrillionth 10(-15th)

Perform the calculation to the correct number of significant figures: 0.987 + 125.1 - 1.22 =

124.867 = 124.9

1 liter (L) = x quarts (qt)

1L = 1.057 qt

1 liter (L) = x milliliters (mL)

1L = 1000 mL

1 liter (L) = x cubic centimeters (cm3)

1L =1000 cm3

1 foot (ft) = x centimeters (cm)

1ft = 30.48cm

1 inch (in) = x centimeters (cm)

1in = 2.54cm

1 kilogram (kg) = x pounds (lb)

1kg = 2.205lb

1 kilometer (km) = x miles (mi)

1km = 0.6214mi

1 pound (lb) = x grams (g)

1lb = 453.59g

1 meter (m) = x yards (yd)

1m = 1.094yd

1 meter (m) = x inches (in)

1m = 39.37in

1 ounce (oz) = x grams (g)

1oz = 28.35g

Express 315,000,000 in scientific notation.

3.15 x 10(8th power)

Express 0.000000000070 in scientific notation.

7.0 x 10(-11th power)

volume

A measure of space. Any unit of length, when cubed, becomes a unit of volume.

mass

A measure of the quantity of matter within an object.

exponent

A number that represents the number of times a term is multiplied by itself. For example in 2(4th power) the exponent is 4 and represents 2 x 2 x 2 x 2.

scientific notation

A system used to write very big or very small numbers, often containing many zeros, more compactly and precisely. A number written in scientific notation consists of a decimal part and an exponential part (10 raised to a particular exponent).

English system

A unit system commonly used in the US

solution map

A visual outline that shows the strategic route required to solve a problem.

How do you calculate density?

Divide the mass of a given amount of the substance by its volume. density = mass/volume (d = m/v)

How do you determine the number of significant numbers involving both multiplication/division and addition/subtraction?

Do the steps in parentheses first; determine the number of significant figures in the intermediate answer; then complete the remaining steps. 3.489 x (5.67 -2.3) Step 1: 5.67 -2.3 = 3.37 (subtraction rule indicates one decimal point which would be two significant numbers) Step 2: 3.489 x 3.37 = 11.758 =12 (since 3.37 in initial step has 1 decimal point, it also has the lease amount of significant numbers in multiplication step, which would make answer 12)

weight

Measure of the gravitational pull on the matter within an object.

decimal part

One part of a number expressed in scientific notation.

exponential part

One part of a number expressed in scientific notation; it represents the number of places the decimal point has moved.

prefix multipliers

Prefixes used by the SI system with the standard units. These multipliers change the value of the unit by powers of 10.

units

Previously agreed-on quantities used to report experimental measurements. Units are vital in chemistry.

meter (m)

The SI standard unit of length.

kilogram (kg)

The SI standard unit of mass.

second (s)

The SI standard unit of time.

SI units

The most convenient system of units for science measurements, based on the metric system. The set of standard units agreed on by scientists throughout the world.

significant figures (digits)

The non-place-holding digits in a reported measurement; they represent the precision of a measured quantity.

What is the correct number of significant figures when multiplying or dividing?

The result carries the same number of significant figures as the factor with the fewest significant figures. 5.02 x 89665 x 10 = 45.0118 = 45 (3 sf) x (5sf) x (2 sf)

What is the correct number of decimal places when adding and subtracting?

The result has the same number of decimal places as the quantity with the fewest decimal places.

International System (SI)

The standard set of units for science measurements, based of the metric system.

metric system

The unit system commonly used throughout most of the world.

Convert 876.9 in(3rd) to m(3rd). a. 0.01437 m(3rd) b. 22.27 m(3rd) c. 5.351 x 10(7th) m(3rd) d. 0.014 m(3rd)

a. 0.01437 m(3rd)

What is the mass of 225 mL of a liquid that has a density of 0.880 g/mL? a. 198 g b. 0.0039 g c. 0.198 g d. 0.256 g

a. 198 g

How many significant numbers are in each number? a. 0.0035 b. 1.080 c. 2371 d. 2.97 x 10(5th) e. 1 dozen =12 f. 100.00 g. 100,000

a. 2 significant numbers ( 3 and 5), leading 0s only mark decimal place. b. 4 significant numbers (interior 0 significant and trailing 0 significant) c. 4 (all nonzero are significant) d. 3 (all nonzeros) e. unlimited (defined numbers are exact and have unlimited number of significant numbers f. 5 significant numbers (non zero (1) and trailing zeros before the decimal point, trailing zeros after the decimal g. ambiguous. write as 1 x 10(5th)

Convert 2855 mg to kg. a. 2.855 x 10(-3rd) kg b. 2.855 kg c. 0.02855 kg d. 3.503 x 10(-4th) kg

a. 2.855 x 10(-3rd) kg

Perform this calculation to the correct number of significant figures: 78.222 x (12.02 - 11.52) a. 39 b. 39.1 c. 39.11 d. 39.111

a. 39

Perform this addition to the correct number of significant figures: 8.32 + 12.148 + 0.02 = a. 20.488 b. 20.49 c. 20.5 d. 21

b. 20.49

A graduated cylinder has markings every milliliter. Which measurement is accurately reported for this graduated cylinder? a. 21 mL b. 21.2 mL c. 21.23 mL d. 21.232 mL

b. 21.2 mL

How many significant figures are in the number 0.00620? a. 2 b. 3 c. 4 d. 5

b. 3

Express the number 0.000042 in scientific notation. a. 0.42 x 10(-4th) b. 4.2 x 10(-5th) c. 4.2 x 10(-4th) d. 4 x 10(-5th)

b. 4.2 x 10(-5th)

A cube measures 2.5 cm on each edge and has a mass of 66.9 g. Calculate the density of the material that composes the cube. (The volume of a cube is equal to the edge length cubed.) a. 10.7 g/cm(3rd) b. 4.3 g/cm(3rd) c. 0.234 g/cm(3rd) d. 26.7 g/cm(3rd)

b. 4.3 g/cm(3rd)

The Curiosity Rover on the surface of Mars recently measured a daily low temperature of -69.19C. What is the implied range of the actual temperature? a. between -65.190C and -65.199C b. between -65.18C and 65.20C c. between -65.1C and -65.2C d. exactly -65.19C

b. The last digit is considered to be uncertain by (+/-) 1

What is the edge length of a 155 g iron cube? (The density of ion is 7.86 g/cm(3rd), and the volume of a cube is equal to the edge length cubed. a. 0.0197 cm b. 19.7 cm c. 1218 cm d. 2.70 cm

d. 2.70 cm

You know that there are 3ft in a yard. How many cubic feet are there in a cubic yard? a. 3 b. 6 c. 9 d. 27

d. 27 (3 ft) x (3 ft) x (3 ft) = 27 ft3

An automobile travels 97.2 km on 7.88 L of gasoline. What is the gas mileage for the automobile in miles per gallon? a. 2.02 mi/gal b. 7.67 mi/gal c. 0.034 mi/gal d. 29.0 mi/gal

d. 29.0 mi/gal

Round the number 89.04997 t three significant figures. a. 89.03 b. 89.04 c. 89.1 d. 89.0

d. 89.0

Convert 76.8 cm to m. a. 0.0768 m b. 7.68 m c. 0.768 m d. 7.68 x 10(-2nd) m

c. 0.768

Perform this multiplication to the correct number of significant figures: 65.2 x 0.0015 x 12.02 = a. 1.17 b. 1.18 c. 1.2 d. 1.176

c. 1.2

A runner runs 4875 ft in 6.85 minutes. What is the runner's average speed in miles per hour? a. 1.34 mi/hr b. 0.0022 mi/hr c. 8.08 mi/hr d. 8.087 mi/hr

c. 8.08 mi/hr