Changing Repeating Decimals to Fractions.notebook
September 23, 2015
Warm up 1. Turn in weekly math to the drawer for a pre-check.
2. Turn in the homework to the drawer.
1
Changing Repeating Decimals to Fractions.notebook
September 23, 2015
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
2
Changing Repeating Decimals to Fractions.notebook
September 23, 2015
1.45
3
Changing Repeating Decimals to Fractions.notebook
September 23, 2015
0.346
4
Changing Repeating Decimals to Fractions.notebook
September 23, 2015
1.042
5
Changing Repeating Decimals to Fractions.notebook
September 23, 2015
0.237
6
Changing Repeating Decimals to Fractions.notebook
September 23, 2015
0.62
7
Changing Repeating Decimals to Fractions.notebook
September 23, 2015
Homework
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
8
Changing Repeating Decimals to Fractions.notebook
September 23, 2015
9