Let's solve each decimal-to-fraction conversion step by step. I'll go through each one, explaining the process.
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General Rules for Converting Decimals to Fractions:
1.
Terminating decimals (end after a few digits):
- Write the decimal as a fraction with the denominator being a power of 10 based on the number of decimal places.
- Simplify the fraction.
2.
Repeating decimals (e.g., $0.\overline{3}$):
- Use algebra to find the fractional form.
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Now, let’s convert each:
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Left Column:
1.
0.45
→ 45/100 =
9/20 (divide numerator and denominator by 5)
2.
0.18
→ 18/100 =
9/50 (divide by 2)
3.
0.3
→ 3/10 =
3/10 (already simplified)
4.
0.95
→ 95/100 =
19/20 (divide by 5)
5.
0.8
→ 8/10 =
4/5 (divide by 2)
6.
0.63
→ 63/100 =
63/100 (no common factors; already simplified)
7.
0.54
→ 54/100 =
27/50 (divide by 2)
8.
0.125
→ 125/1000 =
1/8 (divide by 125)
9.
0.83
→ 83/100 =
83/100 (already simplified)
10.
0.90
→ 90/100 =
9/10 (divide by 10)
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Right Column:
1.
0.285714
→ This is a repeating decimal? Let’s check:
Actually, this looks like
0.285714285714..., which repeats every 6 digits.
But wait — 0.285714 is very close to
2/7 ≈ 0.2857142857...
So:
→
2/7 (exact match for repeating 0.285714...)
2.
0.̄1 → $0.\overline{1}$
Let $ x = 0.\overline{1} $
Then $ 10x = 1.\overline{1} $
Subtract: $ 10x - x = 1.\overline{1} - 0.\overline{1} $ → $ 9x = 1 $ → $ x = \frac{1}{9} $
3.
0.̄3 → $0.\overline{3}$
Let $ x = 0.\overline{3} $
$ 10x = 3.\overline{3} $
$ 10x - x = 3.\overline{3} - 0.\overline{3} $ → $ 9x = 3 $ → $ x = \frac{3}{9} = \frac{1}{3} $
4.
0.16
→ 16/100 =
4/25 (divide by 4)
5.
0.857142
→ Again, this is a repeating decimal: $0.\overline{857142}$
This is known to be
6/7, since:
- $ 6 ÷ 7 = 0.857142857142... $
→ So:
6/7
6.
0.̄4 → $0.\overline{4}$
Let $ x = 0.\overline{4} $
$ 10x = 4.\overline{4} $
$ 10x - x = 4.\overline{4} - 0.\overline{4} $ → $ 9x = 4 $ → $ x = \frac{4}{9} $
7.
0.875
→ 875/1000 =
7/8 (divide by 125)
8.
0.25
→ 25/100 =
1/4
9.
0.428571̄ → $0.428571\overline{1}$? Wait — actually, it's likely meant to be $0.\overline{428571}$, which is
3/7, because:
- $ 3 ÷ 7 = 0.428571428571... $
→ So:
3/7
10.
0.4
→ 4/10 =
2/5
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✔ Final Answers:
| Decimal | Fraction |
|--------|---------|
| 0.45 |
9/20 |
| 0.18 |
9/50 |
| 0.3 |
3/10 |
| 0.95 |
19/20 |
| 0.8 |
4/5 |
| 0.63 |
63/100 |
| 0.54 |
27/50 |
| 0.125 |
1/8 |
| 0.83 |
83/100 |
| 0.90 |
9/10 |
| 0.285714 |
2/7 |
| 0.̄1 |
1/9 |
| 0.̄3 |
1/3 |
| 0.16 |
4/25 |
| 0.857142 |
6/7 |
| 0.̄4 |
4/9 |
| 0.875 |
7/8 |
| 0.25 |
1/4 |
| 0.428571̄ |
3/7 |
| 0.4 |
2/5 |
---
📝 Notes:
- For
repeating decimals, we used algebraic method.
- For
terminating decimals, we converted directly and simplified.
- Some decimals like 0.285714 and 0.857142 are
repeating patterns of fractions involving 7 in the denominator.
Let me know if you'd like a printable version or explanation of any specific problem!
Parent Tip: Review the logic above to help your child master the concept of repeating decimals worksheet.
