Fractions and Decimals • Topic 4 of 7

Converting Fractions to Decimals

To convert a fraction to a decimal, divide the numerator by the denominator. A fraction gives a terminating decimal exactly when its denominator, in lowest terms, has only the prime factors 2 and 5 (for example 1/4 = 0.25, 3/8 = 0.375); any other denominator produces a repeating decimal. Knowing common conversions saves time on the SAT: 1/2 = 0.5, 1/4 = 0.25, 1/5 = 0.2, 1/8 = 0.125, 1/3 = 0.333…. To convert a decimal back to a fraction, write the digits over the matching power of ten and simplify.

✅ Solved examples

1. Convert 3/8 to a decimal.
3 ÷ 8 = 0.375. Since 8 = 2³, the decimal terminates.
2. Convert 0.6 to a fraction in lowest terms.
0.6 = 6/10 = 3/5 after dividing by 2.
3. Will 7/20 terminate?
20 = 2²·5, only factors 2 and 5, so yes — 7/20 = 0.35.
4. Convert 5/4 to a decimal.
5 ÷ 4 = 1.25.

✏️ Practice — try these, take hints as needed

1. Convert 1/8 to a decimal.
Divide 1 by 8.
Add zeros after the decimal point as needed.
1.000 ÷ 8 = 0.125.
0.125.
2. Convert 0.75 to a fraction in lowest terms.
Write 75/100.
Find the GCF of 75 and 100 (it is 25).
Divide both.
3/4.
3. Will 9/40 give a terminating decimal?
Factor 40 into primes.
40 = 2³ · 5 — only 2s and 5s.
Such denominators terminate.
Yes (9/40 = 0.225).
4. Convert 7/25 to a decimal.
25 · 4 = 100.
Multiply numerator and denominator by 4: 28/100.
Write as a decimal.
0.28.
5. Convert 0.04 to a fraction in lowest terms.
Write 4/100.
GCF of 4 and 100 is 4.
Divide both.
1/25.

📝 Topic test — 8 questions

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