Changing Repeating Decimals to Fractions.notebook
September 12, 2016
Writing Repeating Decimals as Fractions
1
2
1
2
4
5
3
3
9
9
9
9
To reverse this process... Follow these steps:
1. Let x equal the repeating decimal that you are trying to
convert into a fraction.
x=
0.5
2. Find the repeating digits in the repeating decimal.
5 is repeating in 0.55555555...
3. Place one or one set of the repeating digit(s) to the left of
the decimal point.
0.555555555... becomes 5.555555555...
4. Determine what power of ten you multiplied the digits by to
get the new number (1 place = 10, 2 places = 100, 3 places = 1000...)
When 0.555555... became 5.5555555... , you multiplied by 10.
x = 0.5555...
10x = 5.5555...
5. Subtract the equations and solve for x.
10x = 5.5
x = 0.5
Changing Repeating Decimals to Fractions.notebook
September 12, 2016
Changing Repeating Decimals to Fractions.notebook
0.45
September 12, 2016
Changing Repeating Decimals to Fractions.notebook
1.23
September 12, 2016
Changing Repeating Decimals to Fractions.notebook
0.346
September 12, 2016
Changing Repeating Decimals to Fractions.notebook
1.042
September 12, 2016
Changing Repeating Decimals to Fractions.notebook
0.237
September 12, 2016
Changing Repeating Decimals to Fractions.notebook
0.62
September 12, 2016
Changing Repeating Decimals to Fractions.notebook
1. 0.6
2. 0.73
3. 1.25
4. 0.624
5. 2.37
6. 0.962
7. 0.87
8. 1.2
9. 2.78
10. 0.95
September 12, 2016
Changing Repeating Decimals to Fractions.notebook
September 12, 2016