Fractions & Decimals • Topic 5 of 5

Fraction–Decimal–Percent Conversions

Fractions, decimals and percents are three names for one value, and fluent conversion is one of the highest-leverage GRE skills. Fraction → decimal: divide top by bottom. Decimal → percent: multiply by 100 (shift the point two places right). Percent → fraction: put it over 100 and reduce (25% = 25/100 = 1/4). The real time-saver is memorising the benchmark table so you recognise values on sight: 1/2 = 0.5 = 50%, 1/3 ≈ 0.333 ≈ 33.3%, 1/4 = 0.25 = 25%, 1/5 = 0.2 = 20%, 1/8 = 0.125 = 12.5%, 3/8 = 0.375 = 37.5%, 2/3 ≈ 0.667 ≈ 66.7%. With that table, "62.5% of 240" becomes (5/8)×240 = 150 in one step, no calculator. Knowing which fractions give terminating decimals (only denominators of the form 2^a·5^b, in lowest terms) also lets you predict a clean vs repeating result before dividing.

✅ Solved examples

1. Convert 5/8 to a decimal and a percent.
5 ÷ 8 = 0.625. Multiply by 100: 62.5%. So 5/8 = 0.625 = 62.5%.
2. Convert 0.35 to a fraction in lowest terms.
0.35 = 35/100. Divide by GCD 5: 7/20. So 0.35 = 7/20.
3. Convert 175% to a fraction and a decimal.
175% = 175/100 = 7/4 (reduce by 25). As a decimal, 7/4 = 1.75.
4. Quantitative Comparison. Quantity A: 3/8. Quantity B: 0.38. Which is greater?
3/8 = 0.375. Compare with 0.38: 0.375 < 0.380, so Quantity B is greater.

✏️ Practice — try these, take hints as needed

1. Convert 7/8 to a decimal.
7 ÷ 8.
Benchmark 1/8 = 0.125.
7 × 0.125.
0.875
2. Convert 0.24 to a fraction in lowest terms.
24/100.
GCD 4.
Reduce.
6/25
3. Convert 3/5 to a percent.
3 ÷ 5 = 0.6.
× 100.
Shift point.
60%
4. Convert 120% to a fraction in lowest terms.
120/100.
GCD 20.
Reduce.
6/5
5. Does 3/16 give a terminating decimal?
16 = 2⁴.
Only 2s and 5s terminate.
Denominator is 2⁴.
Yes (0.1875)

📝 Topic test — 8 questions

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