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**Decimals, Fractions, and Percents**

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

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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% )

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**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.

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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

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**Fractions Fractions can be converted into other forms… Percents**

Decimals

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**Same Value Different Forms**

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

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**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

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**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

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**Convert a decimal into a percentage**

Multiply the decimal by 100: 0.25 x 100 = 25%

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**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%

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**.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)

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**HINTS FRACTIONS DECIMALS PERCENTS 3/4 .75 75% 2/8 .25 25% 3/6 .50 50%**

3/ % 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.

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More Problems…

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Write as a Decimal: 90%

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Answer: 0.9

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Write as a Decimal: %

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Answer:

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Write as a Decimal: 9 %

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Answer: 0.09

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Write as a Decimal: 0.3 %

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Answer:

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Write as a Decimal: ⅗

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Answer: 0.6

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Write as a Decimal: 2⅗

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Answer: 2.6

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Write as a Decimal: 8/33

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Answer: ___ 0.24

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**Write as a Decimal: 4 ²⁷/₁₂₅**

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Answer:

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Write as a Percent:

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Answer: 45.2%

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Write as a Percent:

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Answer: 0.6%

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Write as a Percent: 3.63

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Answer: 363%

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Write as a Fraction: 25%

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Answer: 1/4

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Write as a Fraction: 70%

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Answer: 7/10

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Write as a Fraction: 58%

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Answer: 29/50

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Write as a Fraction: 2.2

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Answer: 2 ⅕

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Write as a Fraction: 0.08

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Answer: 2/25

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Write as a Fraction:

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Answer: 1/200

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Write as a Percent: 1/2

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Answer: 50%

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Write as a Percent: 1/8

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Answer: 12.5%

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Write as a Percent: 2/3

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Answer: 66.6%

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Write as a Percent: 2 ⅟₁₀

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Answer: 210%

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Competition Problems

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**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?

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Answer: 7/20

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Express 5/8 as a percent.

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Answer: 62.5%

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**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?

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Answer: 12%

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

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Answer: 46

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What is 75.5% of 60?

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Answer: 45.3

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What is 35% of 60% of 180?

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Answer: 37.8

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**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?

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Answer: 40%

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**Changing Repeating Decimal to a Fraction**

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

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

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

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

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

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

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

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**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!

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1/9 = … 34/99 = … 248/999 = … 527/999 = … 2471/9999 = … 3278/9999 = … 62653/99999 = … 45341/99999 = … / = … / = …

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

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

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

Notice that the 1st decimal does not repeat, but the remaining do … = 4/ (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)

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

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

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Write as a Fraction: __ 0.3

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Answer: 1/3

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**Write as a Fraction: ____ 0.15**

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Answer: 5/33

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**Write as a Fraction: __ 66.6%**

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Answer: 2/3

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Write as a Fraction: __ 0.35

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Answer: 16/45

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**Write as a Fraction: ____ 0.357**

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Answer: 59/165

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