1. Exercise
Use long division to find the quotient.
180 ÷ 15

2. Exercise
Use long division to find the quotient.
3 ÷ 5

3. Exercise
Use long division to find the quotient.
3 ÷ 12

4. Exercise
Use long division to find the quotient.
1 ÷ 3

5. Exercise
Use long division to find the quotient.
7 ÷ 11

6. , ( ) Rational Numbers can be expressed as a ratio: 3 4 2 1 2
, ( )
3 4
2 1 2
can be expressed as a decimal: , 2

7. When a rational number is expressed as a decimal, the digits either terminate or repeat.

8. 1 3
2 5

9. Example 1
3 4
Convert to a decimal.
0.75
2 8 20
3 4 =
0.75

10. Example 2 5 12 Convert to a decimal. 5 12 = 0.416666… = 0.416 0.416
5 12
Convert to a decimal.
0.416
4 8 20 12 80 72 8
5 12
= …
= 0.416

11. Example 3 2 11 Convert to a decimal. 11 2.00 0.18 1 1 90 88 2 2 11
2 11
Convert to a decimal.
0.18
1 1 90 88 2
2 11
= …
= 0.18

12. Example
Convert the fraction to a decimal.
7 20 =
0.35

13. Example
Convert the fraction to a decimal.
7 3 =
2.3

14. Example
Convert the fraction to a decimal.
4 33 =
0.12

15. Example
Convert the fraction to a decimal. =
0.4583

16. Example
Convert the fraction to a decimal.
5 7 =

17. To convert terminating decimals to fractions: place the digit(s) that follow(s) the decimal point over the place value of the last digit and reduce to lowest terms.

18. Example 4 Convert 0.175 to its reduced rational form using the GCF.
175 1,000 =
7 x x 25
7 40 =

19. Example
Convert 0.12 to a fraction in lowest terms.
12 100
3 25 =

20. Example
Convert 3.25 to a fraction in lowest terms.
13 4 =

21. To convert repeating decimals to fractions:
Set the decimal equal to x.
Multiply the equation by 10n, where n = the number of repeating digits.
Subtract 1. from 2.
Reduce.

22. Example 5
0.45

23. Example 6
0.136

24. 0.3

25. 0.7

26. 0.342

27. 0.571, 0.579, 0.57, 0.6, , , 0.59