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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
2.1.2Converting Terminating Decimals to FractionsConverting Terminating Decimals to Fractions
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
2.1.2Converting Terminating Decimals to FractionsConverting Terminating Decimals to Fractions
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
2.1.2Converting Terminating Decimals to FractionsConverting Terminating Decimals to Fractions
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
2.1.2Converting Terminating Decimals to FractionsConverting Terminating Decimals to Fractions
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
2.1.2Converting Terminating Decimals to FractionsConverting Terminating Decimals to Fractions
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
2.1.2Converting Terminating Decimals to FractionsConverting Terminating Decimals to Fractions
Solution
Convert 0.3497 into a fraction.
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
2.1.2Converting Terminating Decimals to FractionsConverting Terminating Decimals to Fractions
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
2.1.2Converting Terminating Decimals to FractionsConverting Terminating Decimals to Fractions
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
2.1.2Converting Terminating Decimals to FractionsConverting Terminating Decimals to Fractions
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
2.1.2Converting Terminating Decimals to FractionsConverting Terminating Decimals to Fractions
Solution
Convert 0.12 into a fraction.
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
2.1.2Converting Terminating Decimals to FractionsConverting Terminating Decimals to Fractions
Solution
Convert 0.7 into a fraction.
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
2.1.2Converting Terminating Decimals to FractionsConverting Terminating Decimals to Fractions
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
2.1.2Converting Terminating Decimals to FractionsConverting Terminating Decimals to Fractions
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
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Decimals Greater Than 1 Become Improper Fractions
Lesson
2.1.2Converting Terminating Decimals to FractionsConverting Terminating Decimals to Fractions
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
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Example 5
Solution follows…
Lesson
2.1.2Converting Terminating Decimals to FractionsConverting Terminating Decimals to Fractions
7
10Convert 0.7 first — this becomes .
Add on the 13. The result can be written as 13 .7
10
A mixed number.
Solution
Convert 13.7 into a fraction.
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
2.1.2Converting Terminating Decimals to FractionsConverting Terminating Decimals to Fractions
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
19
Independent Practice
Solution follows…
Lesson
2.1.2Converting Terminating Decimals to FractionsConverting Terminating Decimals to Fractions
Convert the decimals given in Exercises 1–10 into fractions without using a calculator.
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
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Independent Practice
Solution follows…
Lesson
2.1.2Converting Terminating Decimals to FractionsConverting Terminating Decimals to Fractions
Convert the decimals given in Exercises 11–20 into fractions without using a calculator.
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
2.1.2Converting Terminating Decimals to FractionsConverting Terminating Decimals to Fractions
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.