statistics mod 2 part 2

Convert 325 grams to kilograms (round to the nearest hundredth)

,33 1000 grams to kilogram divide 325 grams by 1000 for .33 kilograms

Convert −12/48 to a decimal numbe

-0.25 is Correct × Correct. The process stays the same even if the number is negative. Do the calculation as long division, with the numerator set as the dividend and the denominator set as the divisor, and with a decimal point added next to the dividend and another decimal point added at the same location on top of the division bar. Performing the long division, you get −12/48=−0.25. Therefore the answer is −0.25.

−203.8×0.65%

-1.3247

−37.4×31.5%

-11.78

Convert −12.3 to a mixed number

-12 3/10

Convert 97 micrograms to grams

0.000097 1million micro gram to a gram

0.206×50%

0.103 is Correct × Correct. Convert the percentage value to its decimal form by moving the decimal point two places to the left. Write the problem vertically, then multiply like standard decimals. 0.206×50%=0.206×0.50=0.103. Therefore, the answer is 0.103

Convert 7/20 to a decimal number.

0.35 is Correct × Correct. Do the calculation as long division, with the numerator set as the dividend and the denominator set as the divisor, and with a decimal point added next to the dividend and another decimal point added at the same location on top of the division bar. Performing the long division, you get 7/20=0.35. Therefore the answer is 0.35.

Unit Conversions for Household Measures of Volume

1 tablespoon =3 teaspoons 1 fluid ounce =2 tablespoons 1 cup =8 fluid ounces 1 pint =2 cups 1 quart = 2 pints 1 gallon =4 quarts

4.5% of 28

1.26 is Correct × Correct. Set up the percent proportion to solve. Convert 4.5% to its fraction equivalent: 4.5100=x28. Cross multiply (4.5×28)=100x. 126=100x. Solve for x by dividing each side by 100. x=1.26

convert 1,508 milliliters to liters

1.508

Convert 7 quarts to gallons.

1.75 gal. is Correct × Correct. 4 qt. =1 gal. Therefore, 7 qt/.1×1 gal/4 qt.=

Convert 3.5 tablespoons to teaspoons

10.5 tsp. is Correct × Correct. 1 Tbsp. =3 tsp. Therefore,3.5 Tbsp./1×3 tsp./1 Tbsp.

7. Convert 100.95 to a mixed number

100 19/20 is Correct × Correct. The place value occupied by the 5 is the hundredth´s place, so we need a denominator of 100. Remove the decimal point and put 95 over the denominator of 100, then reduce by dividing both the numerator and denominator by 5. 100.95=100 95/100=100(95÷5)(100÷5)=100 19/20. The fraction is reduced to its lowest terms. Therefore the answer is 100 19/20.

20% of 80=

16

Convert 0.684 to a proper fraction

171/250 is Correct × Correct. The place value occupied by the 4 is the thousandth's place, so we need a denominator of 1000. Remove the decimal point and put the 684 over the denominator of 1000, then reduce by dividing both the numerator and denominator by 4. 0.684=684/1000=(684÷4)(1000÷4)=171/250. The fraction is reduced to its lowest terms. Therefore the answer is 171/250.

Convert 18.9 liters to quarts (round to the nearest thousandth).

19.977 qt. is Correct × Correct. 1 L =1.057 qt. Therefore, 18.9 L/1×1.057 qt/.1 L=

300÷150%

200

k/10=120/50 Solve for the variable k

24 is Correct × Correct. We know both denominators, and dividing 50 by 10 produces the conversion number 5. Multiplying both the numerator and denominator of the left fraction by 5 produces (k⋅5)(10⋅5)=12050 or (k⋅5)50=12050. Therefore k⋅5=120. Divide 120 by 5 (120÷5=24), therefore k is 24.

Convert 2.79 grams to milligrams

2790

What would the fractional equivalent of 0.003 be?

3 occupies the thousandths place. This decimal would be read three thousandths. The equivalent fraction would be 3/1000 .

Convert 3-7/20 to a decimal number

3.35 is Correct × Correct. Keep the whole number aside and work only with the fraction part. Do the calculation as long division, with the numerator set as the dividend and the denominator set as the divisor, and with a decimal point added next to the dividend and another decimal point added at the same location on top of the division bar. Performing the long division, you get 7/20=0.35. Now add the whole number back. Therefore the answer is 3.35.

Convert 6.88 pints to quarts

3.44 qt. is Correct × Correct. 2 pt. =1 qt.

. 9.982×35%

3.4937

Convert 7.86 cups to pints

3.93 pt. is Correct × Correct. 2 c. =1 pt.

10. Convert 0.1875 to a proper fraction

3/16 is Correct × Correct. The place value occupied by the 5 is the ten thousandth's place, so we need a denominator of 10,000. Remove the decimal point and put the 1,875 over the denominator of 10,000, then reduce by dividing both the numerator and denominator by 5. 0.1875=187510000=(1875÷5)(10000÷5)=3752000. This fraction can be further reduced by dividing by 25. (375÷25)(2000÷25)=1580. This fraction can be further reduced by dividing by 5. (15÷5)(80÷5)=316. This fraction is reduced to its lowest terms. Therefore the answer is 3/16.

27.2%+3%=

30.2

87.5×42.4%

37.1 is Correct × Correct. Convert the percentage value to its decimal form by moving the decimal point two places to the left. Write the problem vertically, then multiply like standard decimals. 87.5×42.4%=87.5×0.424=37.1. Therefore, the answer is 37.1.

Convert 8.8 Tablespoons to fluid ounces

4.4 fl. oz. is Correct × Correct. There are 2 Tbsp. per fl. oz. Therefore, 8.8 Tbsp./1×1 fl. oz./2 Tbsp.= (8.8 Tbsp.×1 fl. oz.)/(1×2 Tbsp.)= (8.8×1 fl. oz.)2=4.4. Therefore the answer is 4.4 fl. oz.

Convert 0.41 liters to milliliters.

410 ml is Correct × Correct. 1 L =1000 mL.

Convert 20.1 kilograms to poun

44.22 lbs. is Correct × Correct. 1 kg =2.2 l

45÷10%

450

11.5 is 25% of what numbe

46 Correct. Set up the percent proportion to solve. Convert 25% to its fraction equivalent: 25/100=11.5/x. Cross multiply (25x)=(100×11.5). 25x=1150 Solve for x by dividing each side by 25. x=46

What percent of 65 is 32 ? (round your answer to the nearest tenth.)

49.2% Correct. Set up the percent proportion to solve. x/100=32/65. Cross multiply (65x)=(100×32). 65x=3200 Solve for x by dividing each side by 65. x=49.2%

20. 0.55÷1.1%

50

Convert 7.12 to a mixed number

7 3/25 is Correct × Correct. The place value occupied by the 2 is the hundredth´s place, so we need a denominator of 100. Remove the decimal point and put the 12 over the denominator of 100, then reduce by dividing both the numerator and denominator by 2. 7.12=7-12/100=7(12÷2)(100÷2)=7-6/50. The fraction can be further reduced by dividing by 2 again: =7(6÷2)(50÷2)=7-3/25. The fraction is reduced to its lowest terms. Therefore the answer is 7-3/25.

Convert 190.7 pounds to kilograms (round to the nearest hundredeth).

86.68

. 12.63%+75.29%

87.92

Convert 99-102/120 to a decimal number.

99.85 is Correct × Correct. Keep the whole number aside and work only with the fraction part. Do the calculation as long division, with the numerator set as the dividend and the denominator set as the divisor, and with a decimal point added next to the dividend and another decimal point added at the same location on top of the division bar. Performing the long division, you get 102/120=0.85. Now add the whole number back. Therefore the answer is 99.85.

Solving Conditional Proportions

Determine which part of the fraction, the numerator or denominator, has the unknown values. Work with the other part of the fraction, the one with 2 known values. Divide the larger numerator or denominator by the smaller numerator or denominator. We will call the result the conversion number. Multiply this conversion number by both the numerator and denominator of the smaller fraction to establish an equivalent fraction. Match the numerators of the fractions and the denominators of the fractions to solve for the unknown part.

Convert 20/100 to a decimal number

Do the calculation as long division, with the numerator set as the dividend and the denominator set as the divisor, and with a decimal point added next to the dividend and another decimal point added at the same location on top of the division bar. Performing the long division, you get 20/100=0.2. Therefore the answer is 0.2.

medical caduceus symbol When do Nurses Encounter Proportions? Ratio-proportion is an alternative way to figure medication dosages. When using ratio-proportion, you must know how the medication will be supplied or the drug concentration. This information will be found on the medication label. The formula utilized is: Dosage on handAmount on hand = Dosage desiredx Amount desired There are three basic steps to follow when using this formula:

Dosage Calculation Steps All dosages and amounts need to be in the same unit so you may need to convert to equal units. This process will be covered later in this module, but it uses proportions. Estimate the reasonable amount in your head. Complete the calculation. Dosage on hand/Amount on hand = Dosage desiredx /Amount desired

How many mL of a drug is contained in 100 mL of a 1% solution?

First, convert the percentage to a decimal 1100=0.01 . Now multiply that by 100 mL: 0.01×100=1 There is 1 mL of medication

Order (dosage desired): 45 mg po stat Available (dosage on hand): furosemide 20 mg/2 ml liquid.

I think we will give less than 5 ml. 2. Calculate: 1. 20 mg/2 ml = 45 mg/x ml 2. --- 45 mg÷20 mg=2.25 3. (20×2.25)/(2×2.25) ml = 45 mgx ml Solve: x=4-1/2 The dose given to the patient would be 4.5 ml of furosemide.

Rounding Procedures

Identify the digit in the place value to which you are rounding. Evaluate the digit according to the Rounding Rules of Thumb. Rewrite the number from left to right, until you reach the digit being rounded. If this digit is to the left of the decimal, fill in the digits to the right with zeros until you reach the decimal point.

To convert from a decimal to a proper fraction:

Identify the place value for the farthest right number. For example, in the decimal .2078, the digit farthest to the right is an 8. The 8 occupies the ten thousandths place. Place the denominator as the whole number associated with the place value name. Remove the decimal point from the decimal and place as the numerator. Reduce the fraction to lowest terms: Example: Convert 0.50 to a proper fraction: Step 1: The place value occupied by the 5 is the tenth's place. Step 2: We need a denominator of 10 Step 3: Remove the decimal point and put the 5 over the denominator of 10 Step 4: Reduce converting 0.50 to a fraction

Rounding Rules of Thumb

If the digit in the place value to the right of the digit being rounded is 4 or less, the digit being rounded stays the same. If the digit in the place value to the right of the digit being rounded is 5 or greater, add 1 to the digit being rounded.

eample 3/4 = y/12

In order to solve for the variable y , we must find equivalent fractions. Notice that we know both denominators. We divide the 12 by 4 and our conversion number is 3 . We multiply both the numerator and denominator of the smaller fraction by 3 3×3=9 ; 4×3=12

If you find it difficult to see how the feet will cancel in the calculation above, divide the 3 feet by 1 to create a placeholder:

In the example above, you can see how there is a "ft" in both the numerator and denominator. These will cancel in the next step leaving only your desired units.

To convert from a mixed number* to a decimal:

Keep the whole number to one side. Only work with the fraction part. Then, divide the numerator by the denominator as explained on the previous page.

Steps to Calculate a Unit Conversation

List starting units. List desired units. Determine unit conversion rates. Set up fractions so that certain units cancel. Perform calculations and cancel units.

The Butterfly Method

Multiplying across an equality sign is also the method used to establish if two proportions are the same. If the products are equal, the proportion is true. Let's look at the following example to check to see if in fact 4/5 is equal to 20/25 . Because the values of 100 are equal, we know that 4/5 is equal to 20/25 .

Multiplying and Dividing Percentages

Multiplying and dividing percentages require that the percentages be written in decimal form. Once the percentage values are converted to their decimal forms, the rest of the process is like multiplying and dividing decimals. To demonstrate why we need the decimal form of a percentage, consider the problem above. If we multiplied 75×5 ml, we would give the patient 375 ml of the medication, clearly far too much! A percentage less than 100% is only part of the whole, so the percentage needs to be divided by 100 , and after multiplication, the answer will be less than the original amount.

Percentage Of

One very common type of math problem is to determine some percentage of another quantity. For example, if we expect 7% of the population to have type O negative blood and we are collecting blood from 200 volunteers, how many people could we estimate to have type O negative blood? For these types of problems, we convert the percentage to a decimal and then multiply by the quantity. We would find the answer to the question above by converting 7% to a decimal 7100 =0.07 and then multiplying that number by 200 :

To convert from a proper fraction* or an improper fraction* to a decimal.

Place the numerator as the dividend (under the division sign). Be sure to include the decimal point. Place the denominator as the divisor (to the left). Divide. If you are using long division (rather than a calculator), remember to place a decimal point at the end of the denominator. Put the decimal point at the same location on top of the division bar.

rounding

Rounding* is a practice used in all waves of mathematics — from basic arithmetic to economics to health care. It is a method of estimating to make working with a number easier.

what is rounding used for

Rounding* is a practice used in all waves of mathematics — from basic arithmetic to economics to health care. It is a method of estimating to make working with a number easier.

Example: Convert 1079.2078 to a mixed number:

Step 1: The place value occupied by the 8 is the ten thousandths place. Step 2: We need a denominator of 10,000 Step 3: Remove the decimal point and put the 2078 over the denominator of 10,000 Reduce by dividing both the numerator and denominator by 2 .

Example: Convert 10.39 to a mixed number:

Step 1: The place value occupied by the 9 is the hundredth's place. Step 2: We need a denominator of 100 . Step 3: Remove the decimal point and put the 39 over the denominator of 100 . Step 4: The fraction does not need to be reduced. converting 10.39 to a fraction

List desired units.

The purpose of our unit conversion is to represent a value in different units, so we list these units: the desired units.

You can convert from a percentage to a fraction directly.

To convert from a percentage to a fraction: Remove the percentage sign. Put the percentage over 100 . If you have a decimal within the percentage, remove it by multiplying the numerator and denominator by as many 10 s as are needed. Reduce the fraction to lowest terms

Convert a Percentage to a Decimal

To find the decimal equivalent of a percentage, you simply move the decimal point two places to the left, that is you are dividing by 100 . Any number divided by 100 will have a decimal point moved 2 places to the left. The same rules go for percentages with decimals. For example, 86.25% would equal .8625 . Percentages have to be converted to decimals for division problems as well. If you are dividing by 50% , you will be dividing by 0.5 (or 50÷100 ). Now that we can convert 75% of a medication ("of" almost always signals multiplication), we can multiply 0.75×5=3.75 ml.

set up fractions so that cups cancel.s

To perform a unit conversion, we need to cancel the units that we don't want in our final measurement. The units that we want in our final representation should not cancel. Here, that means we want to cancel cups. We already have cups in the numerator; we need a fraction with cups in the denominator. The fraction that is set up to facilitate canceling out the units that we do not want is called a unit multiplier. First, we have our initial volume in cups, written as a fraction:

List starting units.

Unit conversion is performed when we are given a measurement in one unit system, but we need to convert to a different measurement. The first step in unit conversion is to list the units that we are initially given: the starting units.

Set up equation with unit multiplier fractions.

Unit conversions are executed by unit cancellation*. If units divide one another, they cancel each other out. Therefore, units cancel if there is an instance of a unit in the numerator and the same unit in the denominator of a fraction.

20/16=x/4 Solve for the variable x

We know both denominators, and dividing 16 by 4 produces the conversion number 4. Multiplying both the numerator and denominator of the right fraction by 4 produces 20/16=(x⋅4)(/4⋅4) or 20/16=(x⋅4)16. Therefore, 20=x⋅4. Divide 20 by 4 (20÷4=5), therefore x=5.

Determine unit conversion rates

When converting between different units, you need to know the conversion rates. For example:

unit multiplier fraction*

When performing unit conversions, we want to set the problem up so that we can cancel the units we don't want in our final measurement. Our desired units — the units that we want in our final representation — should not cancel. To accomplish this, we create a special fraction called a unit multiplier fraction* and multiply it by our original fraction. The most challenging step in converting units is deciding which units go in the numerator and which in the denominator.

Division with Decimals

Write the problem so the dividend is under the division symbol and the divisor is to the left of the symbol. If the number in the dividend is an integer, put a decimal point next to the units place. Convert the divisor to a whole number by moving the decimal point to the right as many places as are needed. Move the decimal point in the dividend the same number of places. Add zeros if necessary. Place a decimal point for the answer (quotient) directly above the decimal point of dividend, above the division bar. Divide as you would for whole numbers.

IAdding or Subtracting Decimals

Write the problem vertically, lining up the decimal points. Fill in the missing decimal places with zeros as placeholders. Add or subtract as you would whole numbers. Bring down the decimal point. Write the answer, dropping any trailing zeros which follow the decimal point (if any).

Multiplying Decimals

Write the problem vertically, writing the decimal with the most digits on the top. Multiply the two decimals as you would if you were multiplying whole numbers. Determine the number of decimal places in both factors. Working from the far right to left count the number of places that correspond to the number of decimal places needed and put in a decimal point. Write the answer, dropping any trailing zeros which follow the decimal point (if any).

An example of this type of problem is the question "What percentage is 3 of 4 ?" Here the ratio 3 over 4 is set equal to x/100 .

You solve these problems either through the butterfly method of cross-multiplication after you have set up the proportion for the unknown or by finding an equivalent fraction, whichever process is easiest for you. x=75

3 ft - 12in/1 ft

let's look at converting 3 feet to a certain number of inches. To do this, we need to add a unit multiplier that will cancel out the feet units and give us an answer in inches. The conversion rate is 1ft=12 inches. We need to create a fraction with feet and inches that will allow us to cancel the feet.

metric measure conversion

liter (L) 1 L =1000 mL 1 L/1000 mL Milliliter (mL) 1 mL =0.001 L Kilograms 1 kg =1000 g Gram (g) 1 g =0.001 kg Milligram (mg) 1 mg =0.001 g Microgram (mcg) 1 mcg =0.000001 g

percentages

Denoted by the percent sign*, % , percentages are also part of whole — but that whole is 100 . When you see a number with a percent sign, it is a percent — or a part — of 100 . Unlike decimals or fractions, percentages must be used in conjunction with other quantities or entities. We do not say "the value is 50% ," but rather " 50% of the IV drip" (or some other percent value).

adding and subtracting percentages

Adding and subtracting percentages is similar to adding and subtracting whole numbers and decimals. 42.5%+16%=58.5%

The Percent Proportion

As we have learned, a percent is a part of 100 . The percent proportion* is a way of converting a percentage into a proportion. You need this in order to find percentages of quantities. To set up the percent proportion, you express the percentage over 100 . So 70% would be 70100 . Writing a percentage as a proportion helps solve a certain type of percentage problem. The proportion can be set equal to an amount x amount over y . Here, x and y would represent the ratio you are given, and the percent is the part of 100 (variable) you are trying to solve for.

Conversions between Household and Metric Measures

Cubic Centimeters ( cm3 ) and Milliliters (mL) 1 cubic centimeter =1 milliliter There is no need to convert because the two are equal Fluid Ounces (fl. oz.) and Milliliters (mL) 1 fluid ounce =30 mL Liters (L) and Quarts (qt.) 1 liter =1.057 quarts Teaspoons (tsp.) and Milliliters (mL) 1 teaspoon =5 milliliters Kilograms (kg) and Pounds (lb.) 1 kilogram =2.2 pounds Ounces (oz.) and grams (g) 1 ounce =28.35 grams

converting cup to ounces cont

Determine unit conversion rates. The starting unit is cups and the desired unit is fluid ounces. So, we need to convert between cups and fluid ounces. The conversion rate for cups to ounces is: 1 cup =8 fluid ounces.

decimals

Decimals are denoted by a decimal point, which will fall on the right side of a whole number. The part of the whole is determined by how many numbers fall to the right of the decimal point.

Unit conversion*

is converting a measurement in one scale to one in a different scale. For example, you might be given a length measurement in centimeters and need to convert it to inches. Unit conversion is a very important math skill in nursing.

Conditional Proportions

conditional proportion* is when one part of a proportion is a variable or unknown quantity. To solve a conditional proportion, follow the steps below:

1.5

n the above example, 1 is the whole number* and .5 is the decimal. In this example, 5 is in the tenths place, which translates to "five tenths" or 510 (fractions!). We read the decimal point as and, so this number would be read "one and five tenths." In the example below, we expand the decimal further to the right. Two places to the right of the decimal point is known as the hundredths place. In the examples below, we have 5 in the tenths place or 510 ; 53 in the hundredths place, or 53100 . Therefore this number would be read as "one and fifty-three hundredths." Finally, we have 538 in the thousandths place or 5381000 Therefore 1.538 would be read as "one and five hundred thirty-eight thousandths."

Convert 3 cups to fluid ounces.

o perform the unit conversion, follow the steps. 1. List starting units. Here we are converting the household volume measurement of 3 cups, to the volume measurement fluid ounces. Let's take inventory of our starting units: Starting Units = Cups Initially, we know the volume in cups. 2. List desired units. Now we list the desired units: Desired Units=Ounces We want to represent the amount of liquid volume in ounces.

proportion

proportion* is a true statement in which two ratios are equal to each other. For example, the expression four-fifths is equal to twenty twenty-fifths is a proportion as illustrated below. Proportions can be used when comparing two ratios, frequently concluding that they are equal or unequal. Two ratios are said to be "proportional" if they are equivalent. An example could be comparing the amount of drug x in a solution. If solution A has 25 mg of drug x per .5 liter and solution B has 50 mg of drug x per liter both solutions would be equal to 50 mg per liter of drug x . These solutions would be proportional in their percent of drug x

rate

rate is a ratio that compares two quantities having different units of measure. For example, a nurse might be asked to give a certain amount of medicine in milligrams per hour for a given patient's body weight. The dosage for the medicine, however, is given in micrograms per kilogram. So in order to know how much the patient should receive, the micrograms need to be converted to milligrams. This is an example of a rate.

Proportions and Unknown Quantity

ratio* is a comparison of two numbers. This comparison can be written in a variety of different ways, each expressing that for every x amount of this you have y amount of that. The example below illustrates that for every 4 of one item, we have 5 of another item.

True or False? Ratios that are unequal are proportional.

this is a false statement. Two ratios are proportional only if they are equivalent.

"what number is 36% of 20 ?"

x=7.2

300/200=120/z Solve the following for the variable z

z=80 We know both numerators, and dividing 300 by 120 produces the conversion number 2.5. Multiplying both the numerator and denominator of the right fraction by 2.5 produces 300/200=(120⋅2.5)(z⋅2.5) or 300/200=300(z⋅2.5). Therefore, 200=z⋅2.5. Divide 200 by 2.5 (200÷2.5=80), therefore z is 80.