1 lesson 2.1.2 converting terminating decimals to fractions converting terminating decimals to...

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Lesson 2.1.2Lesson 2.1.2

Converting TerminatingDecimals to Fractions

Converting TerminatingDecimals to Fractions

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Lesson

2.1.2Converting Terminating Decimals to FractionsConverting Terminating Decimals to Fractions

California Standard:Number Sense 1.5Know that every rational number is either a terminating or a repeating decimal and be able to convert terminating decimals into reduced fractions.

What it means for you:

Key Words:

You’ll see how to change terminating decimals into fractions that have the same value.

• fraction• decimal• terminating

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Lesson


This Lesson is a bit like the opposite of the last Lesson — you’ll be taking decimals and finding their equivalent fractions.

This is how you can show that they’re definitely rational numbers.

0.51

2

0.1251

8

4

Decimals Can Be Turned into Fractions

Lesson


If you read decimals using the place-value system, then it’s more straightforward to convert them into fractions.

0.15 is said “fifteen-hundredths,”

so it turns into the fraction .15

100

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Lesson


You need to remember the value of each position after the decimal point:

0.1234

tenthshundredths thousandths

ten-thousandths

decimal point

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Then when you are reading a decimal number, look at the position of the last digit.

Lesson


0.01 is one-hundredth, which is the fraction .1

100

0.1 is one-tenth, which is the fraction .1

10

7

Example 1

Solution follows…

Lesson


Solution

Convert 0.27 into a fraction.

0.27 is twenty-seven hundredths, so it is .27

1000.27 is twenty-seven hundredths,

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Example 2

Solution follows…

Lesson


Solution


0.3497 is 3497 ten-thousandths, so it is .3497

10,0000.3497 is 3497 ten-thousandths,

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Guided Practice

Solution follows…

Lesson


Convert the decimals in Exercises 1–12 into fractions without using a calculator.

1. 0.1 2. 0.23 3. 0.17

4. –0.87 5. 0.7 6. 0.35

7. 0.174 8. –0.364 9. 0.127

10. 0.9827 11. 0.5212 12. –0.4454

1

10

23

100

17

100

–87

100

7

10

35

100

174

1000

127

1000

–364

1000

9827

10,000

5212

10,000

–4454

10,000

10

When you convert decimals to fractions this way, you’ll often get fractions that aren’t in their simplest form.

Some Fractions Can Be Made Simpler

Lesson


If an answer is a fraction, you should usually give it in its simplest form.

could be written more simply as5

10

1

2

could be written more simply as75

100

3

4

11

This is how to reduce a fraction to its simplest form:

Lesson


1. Find the biggest number that will divide into both the numerator and the denominator without leaving any remainder.

2. Then divide both the numerator and the denominator by the GCF.

This number is called the greatest common factor, or GCF.

If the greatest common factor is 1 then the fraction is already in its simplest form — you can’t simplify it any more.

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0.12 is twelve hundredths.

Example 3

Solution follows…

Lesson


Solution


As a fraction it is .12

100

The factors of 12 are 1, 2, 3, 4, 6, and 12. The biggest of these that also divides into 100 leaving no remainder is 4.

Divide both the numerator and denominator by 4.

So the greatest common factor of 12 and 100 is 4.

0.12 as a fraction in its simplest form is .3

25

12 ÷ 4

100 ÷ 4

3

25=

13

Example 4

Solution follows…

Lesson


Solution


0.7 is seven tenths. As a fraction it is .7

10

The greatest common factor of 7 and 10 is 1, so this fraction is already in its simplest form.

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Guided Practice

Solution follows…

Lesson


Convert the decimals in Exercises 13–20 into fractions and then simplify them if possible.

13. 0.25 14. 0.65

15. –0.02 16. 0.256

17. 0.0175 18. –0.84

19. 0.267 20. 0.866

1

4

13

20

–1

50

–21

25

32

125

7

400

267

1000

433

500

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Guided Practice

Solution follows…

Lesson


21. Priscilla measures a paper clip. She decides that it is six-eighths of an inch long. Otis measures the same paper clip with a different ruler and says it is twelve-sixteenths of an inch long. How can their different answers be explained?

is a simpler form of . Both answers are the same.6

8

12

16

16

Decimals Greater Than 1 Become Improper Fractions

Lesson


When you convert a decimal number greater than 1 into a fraction it’s probably easier to change it into a mixed number first.

Then you can change the mixed number into an improper fraction.

1.51

21

3

2

17

Example 5

Solution follows…

Lesson


7

10Convert 0.7 first — this becomes .

Add on the 13. The result can be written as 13 .7

10

A mixed number.

Solution


So add to this:

13 whole units are equivalent to .13

1

10

10• =

130

1013

1

10

10• + = + =

7

10

130

10

7

10

137

10

7

10

Now turn 13 into an improper fraction.7

10

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Guided Practice

Solution follows…

Lesson


Convert the decimals given in Exercises 22–33 into fractions without using a calculator.

22. 4.3 23. –1.03 24. 15.98

25. –1.7 26. 9.7 27. –4.5

28. 12.904 29. –13.142 30. –8.217

31. 0.3627 32. 1.8028 33. 4.1234

43

10

–103

100

799

50

–17

10

97

10

–9

2

1613

25

–8217

1000

–6571

500

3627

10,000

4507

2500

20,617

5000

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Independent Practice

Solution follows…

Lesson



1. 0.3 2. 0.2

3. 0.4 4. 0.30

5. 0.26 6. 0.18

7. –0.34 8. –1.34

9. 0.234 10. 2.234

3

10

117

100

1

5

3

10

1117

500

2

5

13

50

9

50

–17

50

–67

50

20

Independent Practice

Solution follows…

Lesson



11. 9.140 12. 3.655

13. –0.121 14. –0.655

15. –10.760 16. 5.001

17. 0.2985 18. 2.3222

19. –9.3452 20. –0.2400

457

50

–6

25

731

200

–121

1000

–131

200

–269

25

5001

1000

597

2000

11,611

5000

–23,363

2500

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Round UpRound Up

Lesson


The important thing when converting a decimal to a fraction is to think about the place value of the last digit. Then read the decimal and turn it into a fraction.

If the decimal is greater than 1, ignore the whole number until you get the decimal part figured out.

Take your time, do each step carefully, and you should be OK.

1 lesson 2.1.2 converting terminating decimals to fractions converting terminating decimals to...

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