I need to convert repeating decimals to fractions. Since the user didn't request explanations, teaching, or practice, I'll just solve all 16 problems and provide the final answers.
Let me work through each one:
Problem 1: 3.33...
Let x = 3.33...
10x = 33.33...
10x - x = 33.33... - 3.33...
9x = 30
x = 30/9 = 10/3
Problem 2: 8.999...
Let x = 8.999...
10x = 89.999...
10x - x = 89.999... - 8.999...
9x = 81
x = 81/9 = 9
Problem 3: 1.2525...
Let x = 1.2525...
100x = 125.2525...
100x - x = 125.2525... - 1.2525...
99x = 124
x = 124/99
Problem 4: 0.888...
Let x = 0.888...
10x = 8.888...
10x - x = 8.888... - 0.888...
9x = 8
x = 8/9
Problem 5: 0.1717...
Let x = 0.1717...
100x = 17.1717...
100x - x = 17.1717... - 0.1717...
99x = 17
x = 17/99
Problem 6: 0.9999...
Let x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 9/9 = 1
Problem 7: 10.9898...
Let x = 10.9898...
100x = 1098.9898...
100x - x = 1098.9898... - 10.9898...
99x = 1088
x = 1088/99
Problem 8: 1.4444...
Let x = 1.4444...
10x = 14.4444...
10x - x = 14.4444... - 1.4444...
9x = 13
x = 13/9
Problem 9: 11.111...
Let x = 11.111...
10x = 111.111...
10x - x = 111.111... - 11.111...
9x = 100
x = 100/9
Problem 10: 0.8787...
Let x = 0.8787...
100x = 87.8787...
100x - x = 87.8787... - 0.8787...
99x = 87
x = 87/99 = 29/33
Problem 11: 0.1222...
Let x = 0.1222...
10x = 1.222...
100x = 12.222...
100x - 10x = 12.222... - 1.222...
90x = 11
x = 11/90
Problem 12: 0.444...
Let x = 0.444...
10x = 4.444...
10x - x = 4.444... - 0.444...
9x = 4
x = 4/9
Problem 13: 125.777...
Let x = 125.777...
10x = 1257.777...
10x - x = 1257.777... - 125.777...
9x = 1132
x = 1132/9
Problem 14: 99.2323...
Let x = 99.2323...
100x = 9923.2323...
100x - x = 9923.2323... - 99.2323...
99x = 9824
x = 9824/99
Problem 15: 0.1111...
Let x = 0.1111...
10x = 1.1111...
10x - x = 1.1111... - 0.1111...
9x = 1
x = 1/9
Problem 16: 0.555...
Let x = 0.555...
10x = 5.555...
10x - x = 5.555... - 0.555...
9x = 5
x = 5/9
Final Answer:
1. 10/3
2. 9
3. 124/99
4. 8/9
5. 17/99
6. 1
7. 1088/99
8. 13/9
9. 100/9
10. 29/33
11. 11/90
12. 4/9
13. 1132/9
14. 9824/99
15. 1/9
16. 5/9
Parent Tip: Review the logic above to help your child master the concept of convert decimals to fractions worksheet pdf.
