1. Converting Terminating
Decimals to Fractions
Lesson 2.1.2

2. 2.1.2 Converting Terminating Decimals to Fractions
Lesson
2.1.2
Converting Terminating Decimals to Fractions
California Standard:
Number Sense 1.5
Know 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:
You’ll see how to change terminating decimals into fractions that have the same value.
Key Words:
fraction
decimal
terminating

3. 2.1.2 Converting Terminating Decimals to Fractions
Lesson
2.1.2
Converting 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.
0.5 1 2
0.125 1 8
This is how you can show that they’re definitely rational numbers.

4. 2.1.2 Converting Terminating Decimals to Fractions
Lesson
2.1.2
Converting Terminating Decimals to Fractions
Decimals Can Be Turned into 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

5. 2.1.2 Converting Terminating Decimals to Fractions
Lesson
2.1.2
Converting Terminating Decimals to Fractions
You need to remember the value of each position after the decimal point:
decimal point
0.1234
tenths
ten-thousandths
hundredths
thousandths

6. 2.1.2 Converting Terminating Decimals to Fractions
Lesson
2.1.2
Converting Terminating Decimals to Fractions
Then when you are reading a decimal number, look at the position of the last digit.
0.1 is one-tenth, which is the fraction . 1 10
0.01 is one-hundredth, which is the fraction 1
100

7. 2.1.2 Converting Terminating Decimals to Fractions
Lesson
2.1.2
Converting Terminating Decimals to Fractions
Example 1
Convert 0.27 into a fraction.
Solution
0.27 is twenty-seven hundredths, so it is 27
100
0.27 is twenty-seven hundredths,
Solution follows…

8. 2.1.2 Converting Terminating Decimals to Fractions
Lesson
2.1.2
Converting Terminating Decimals to Fractions
Example 2
Convert into a fraction.
Solution
is 3497 ten-thousandths, so it is
3497
10,000
is 3497 ten-thousandths,
Solution follows…

9. 2.1.2 Converting Terminating Decimals to Fractions Guided Practice
Lesson
2.1.2
Converting Terminating Decimals to Fractions
Guided Practice
Convert the decimals in Exercises 1–12 into fractions without using a calculator.
4. – –
–0.4454 1 10 23
100 17
100
–87
100 7 10 35
100
174
1000
–364
1000
127
1000
9827
10,000
5212
10,000
–4454
10,000
Solution follows…

10. 2.1.2 Converting Terminating Decimals to Fractions
Lesson
2.1.2
Converting Terminating Decimals to Fractions
Some Fractions Can Be Made Simpler
When you convert decimals to fractions this way, you’ll often get fractions that aren’t in their simplest form.
could be written more simply as 5 10 1 2 75
100 3 4
If an answer is a fraction, you should usually give it in its simplest form.

11. 2.1.2 Converting Terminating Decimals to Fractions
Lesson
2.1.2
Converting Terminating Decimals to Fractions
This is how to reduce a fraction to its simplest form:
Find the biggest number that will divide into both the numerator and the denominator without leaving any remainder.
This number is called the greatest common factor, or GCF.
Then divide both the numerator and the denominator by the GCF.
If the greatest common factor is 1 then the fraction is already in its simplest form — you can’t simplify it any more.

12. 2.1.2 Converting Terminating Decimals to Fractions
Lesson
2.1.2
Converting Terminating Decimals to Fractions
Example 3
Convert 0.12 into a fraction.
Solution
As a fraction it is 12
100
0.12 is twelve hundredths.
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.
So the greatest common factor of 12 and 100 is 4.
Divide both the numerator and denominator by 4.
12 ÷ 4
100 ÷ 4 3 25 =
0.12 as a fraction in its simplest form is 3 25
Solution follows…

13. 2.1.2 Converting Terminating Decimals to Fractions
Lesson
2.1.2
Converting Terminating Decimals to Fractions
Example 4
Convert 0.7 into a fraction.
Solution
As a fraction it is . 7 10
0.7 is seven tenths.
The greatest common factor of 7 and 10 is 1, so this fraction is already in its simplest form.
Solution follows…

14. 2.1.2 Converting Terminating Decimals to Fractions Guided Practice
Lesson
2.1.2
Converting Terminating Decimals to Fractions
Guided Practice
Convert the decimals in Exercises 13–20 into fractions and then simplify them if possible.
15. –
–0.84 1 4 13 20 –1 50 32
125 7
400
–21 25
267
1000
433
500
Solution follows…

15. 2.1.2 Converting Terminating Decimals to Fractions Guided Practice
Lesson
2.1.2
Converting Terminating Decimals to Fractions
Guided Practice
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
Solution follows…

16. 2.1.2 Converting Terminating Decimals to Fractions
Lesson
2.1.2
Converting Terminating Decimals to Fractions
Decimals Greater Than 1 Become Improper 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 2 3 2
1.5

17. 2.1.2 Converting Terminating Decimals to Fractions
Lesson
2.1.2
Converting Terminating Decimals to Fractions
Example 5
Convert 13.7 into a fraction.
Solution 7 10
Convert 0.7 first — this becomes .
A mixed number.
Add on the 13. The result can be written as 7 10
Now turn into an improper fraction. 7 10
13 whole units are equivalent to 13 1 10
• =
130 7 10 13 1 10
• = = 7
130
137
So add to this:
Solution follows…

18. 2.1.2 Converting Terminating Decimals to Fractions Guided Practice
Lesson
2.1.2
Converting Terminating Decimals to Fractions
Guided Practice
Convert the decimals given in Exercises 22–33 into fractions without using a calculator. –
25. – –4.5
– –8.217 43 10
–103
100
799 50
–17 10 97 10 –9 2
1613 25
–6571
500
–8217
1000
3627
10,000
4507
2500
20,617
5000
Solution follows…

19. 2.1.2 Converting Terminating Decimals to Fractions
Lesson
2.1.2
Converting Terminating Decimals to Fractions
Independent Practice
Convert the decimals given in Exercises 1–10 into fractions without using a calculator.
7. – –1.34 3 10 1 5 2 5 3 10 13 50 9 50
–17 50
–67 50
117
100
1117
500
Solution follows…

20. 2.1.2 Converting Terminating Decimals to Fractions
Lesson
2.1.2
Converting Terminating Decimals to Fractions
Independent Practice
Convert the decimals given in Exercises 11–20 into fractions without using a calculator.
13. – –0.655
15. –
19. – –0.2400
457 50
731
200
–121
1000
–131
200
–269 25
5001
1000
597
2000
11,611
5000
–23,363
2500 –6 25
Solution follows…

21. 2.1.2 Converting Terminating Decimals to Fractions Round Up
Lesson
2.1.2
Converting Terminating Decimals to Fractions
Round Up
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.