Decimals, Fractions, and Percents

Session Outcomes: To identify equivalences between fractions, decimals and percent. To identify the relationship between fractions, decimals and percent. May 2011. Kindly contributed to www.skillsworkshop.org by Helen Holt, Lincoln College.

Definitions Decimal - Any number shown with a decimal point; a number based upon tenths or hundredths. ( 0.2, 0.375, 86.4 ) Fraction - One or more of the equal parts of a whole; a number usually expressed in the form a/b. ( 1/3, 2 5/8, 7/4 ) Percent- The word percent comes from Latin and means “ for each hundred” or “ per hundred.” ( 70%, 6.5%, 4.09% )

What are fractions, decimals,and percents? Fractions, decimals and percents are different ways of representing part of a whole. We could say 50% of something, or ½, or 0.5. These are all the same quantity.

What are fractions? A fraction describes part of a whole when the whole is cut into equal parts. This circle has been cut into four equal parts. These equal parts are called fourths. A fourth is written as: ¼ The three red sections equal three fourths, which would be written as: ¾ ¼   

Fractions Fractions can be converted into other forms… Percents Decimals

Same Value Different Forms A same value can be written in different forms. For example: ½ fraction .5 decimal 50% percent

Convert a fraction into a decimal Divide the top of the fraction(numerator) by the bottom (denominator) of the fraction: ½ = 1÷2 = 0.5

Time to try converting a fraction into a decimal. Fraction to convert = 3/4 Divide 3(numerator) ÷ 4(denominator) Answer = .75 3/4 is equivlent to .75

Convert a decimal into a percentage Multiply the decimal by 100: 0.25 x 100 = 25%

Time to try converting a decimal into a percent. Decimal to convert = .75 Multiply the decimal by 100 .75 x 100 3. Answer = 75% .75 is equivalent to 75%

.75 or 75% or 75/100 (which reduces to ¾) 75 out of 100 squares are shaded. .75 or 75% or 75/100 (which reduces to ¾)

HINTS FRACTIONS DECIMALS PERCENTS 3/4 .75 75% 2/8 .25 25% 3/6 .50 50% 3/4 .75 75% 2/8 .25 25% 3/6 .50 50% 3/10 .30 30% 2/5 .40 40% HINTS Fraction to a decimal = Divide the numerator (top) by the denominator (bottom). Decimal to a percent = Multiple the decimal by 100.

More Problems…

Write as a Decimal: 90%

Answer: 0.9

Write as a Decimal: 115.9 %

Answer: 1.159

Write as a Decimal: 9 %

Answer: 0.09

Write as a Decimal: 0.3 %

Answer: 0.003

Write as a Decimal: ⅗

Answer: 0.6

Write as a Decimal: 2⅗

Answer: 2.6

Write as a Decimal: 8/33

Answer: ___ 0.24

Write as a Decimal: 4 ²⁷/₁₂₅

Answer: 4.216

Write as a Percent: 0.452

Answer: 45.2%

Write as a Percent: 0.006

Answer: 0.6%

Write as a Percent: 3.63

Answer: 363%

Write as a Fraction: 25%

Answer: 1/4

Write as a Fraction: 70%

Answer: 7/10

Write as a Fraction: 58%

Answer: 29/50

Write as a Fraction: 2.2

Answer: 2 ⅕

Write as a Fraction: 0.08

Answer: 2/25

Write as a Fraction: 0.005

Answer: 1/200

Write as a Percent: 1/2

Answer: 50%

Write as a Percent: 1/8

Answer: 12.5%

Write as a Percent: 2/3

Answer: 66.6%

Write as a Percent: 2 ⅟₁₀

Answer: 210%

Competition Problems

65% of the Student Council members voted yes on a survey 65% of the Student Council members voted yes on a survey. What fraction voted no?

Answer: 7/20

Express 5/8 as a percent.

Answer: 62.5%

On Brennan’s test, he got 22 out of 25 questions correct On Brennan’s test, he got 22 out of 25 questions correct. What percentage did he answer incorrectly?

Answer: 12%

Find 80% of 115. Find 50% of that number.

Answer: 46

What is 75.5% of 60?

Answer: 45.3

What is 35% of 60% of 180?

Answer: 37.8

Three-fifths of the students made at least an 83 on the exam Three-fifths of the students made at least an 83 on the exam. What percent of the students did not make at least an 83?

Answer: 40%

Changing Repeating Decimal to a Fraction

Let’s recall how we write repeating decimals. 1111111… = 0. 1 0

Use your calculator and check a few fractions: 1/9 = 0

So… Can you see the pattern. 1111111… = 0. 1 0. 2222222… = 0. 2 0

So… Can you see the pattern. 1111111… = 0. 1 = 1/9 0. 2222222… = 0

Use your calculator and check a few more fractions: 12/99 = 0

Use your calculator and check a few more fractions: 24/99 = 0

Use your calculator and check a few more fractions: 248/999 = 0

So… Can you see the pattern So… Can you see the pattern? If all the decimals repeat, then just place a “9” under each number to complete the fraction!

1/9 = 0.1111111… 34/99 = 0.3434343434… 248/999 = 0.248248248248… 527/999 = 0.527527527527… 2471/9999 = 0.247124712471… 3278/9999 = 0.327832783278… 62653/99999 = 0.626536265362653… 45341/99999 = 0.453414534145341… 157899/999999 = 0.157899157899157899… 8521967/9999999 = 0.852196785219678521967…

Let’s look at a little more complicated repeating decimal. 0.455555555… 0.277777777… 0.166666666…

Notice that the 1st decimal does not repeat, but the remaining do

Notice that the 1st decimal does not repeat, but the remaining do Notice that the 1st decimal does not repeat, but the remaining do. 0.4 + 0.055555… = 4/10 + 0.0(5/9) = 2/5 + (5/9)·(1/10) = 2/5 + (5·1)/(9·10) = 2/5 + 5/90 = 36/90 + 5/90 = 41/90 (use a calculator to check your answer)

We can do this with any repeating decimal. 127455555555… = 0. 1274 + 0

We can do this with any repeating decimal. 127453535353… = 0. 1274 + 0

Write as a Fraction: __ 0.3

Answer: 1/3

Write as a Fraction: ____ 0.15

Answer: 5/33

Write as a Fraction: __ 66.6%

Answer: 2/3

Write as a Fraction: __ 0.35

Answer: 16/45

Write as a Fraction: ____ 0.357

Answer: 59/165