Curriculum Core Rules & Strategy
Always write out given values and the relevant formula before substituting numbers.
Substitute your final answer back into the original problem to verify correctness.
Double-check negative signs, common denominators, and arithmetic order of operations.
Mastering Fractions to Decimals with SolveCalc
Every fraction produces either a terminating decimal (finite digits) or a repeating decimal (infinitely repeating block). The denominator determines which: only factors of 2 and 5 give terminating decimals in base 10.
Division is the Foundation
Converting a fraction to a decimal is, at its heart, a division problem: divide the numerator by the denominator.
- 3/4 = 3 ÷ 4 = 0.75 (terminating)
- 1/3 = 1 ÷ 3 = 0.333... (repeating, written 0.3̄)
- 2/7 = 2 ÷ 7 = 0.285714285714... (repeating with period 6)
Whether a fraction terminates or repeats depends entirely on the denominator (when the fraction is in lowest terms).
Predicting Whether a Decimal Terminates
A fraction p/q (in lowest terms) produces a terminating decimal if and only if q has no prime factors other than 2 and 5.
- 1/8: 8 = 2³ → terminating (0.125)
- 3/20: 20 = 2² × 5 → terminating (0.15)
- 1/6: 6 = 2 × 3 → repeating (0.1666...) — has a factor of 3
- 5/7: 7 is prime (≠2, ≠5) → repeating (0.714285...)
This rule works because our number system is base-10 = 2 × 5. Only fractions whose denominators are made exclusively from 2s and 5s can be expressed as exact decimal fractions.
Long Division for Fraction Conversion
To convert 5/11 to a decimal using long division:
- Write 5.000000 ÷ 11
- 11 goes into 50 four times (44), remainder 6
- 11 goes into 60 five times (55), remainder 5
- 11 goes into 50 four times again — the remainder repeats!
The period (length of the repeating block) is always less than the denominator. For 1/7, the maximum period is 6.
Three Fraction-to-Decimal Conversions
8 = 2³ → terminating. 7÷8 = 0.875
9 = 3² → repeating. 4÷9 = 0.444... = 0.4̄
3/8 = 0.375. 0.375 < 0.4. Yes, the pipe fits (with 0.025 inch to spare).
SolveCalc Insight
DEEP DIVESolveCalc provides free, browser-based math tools for students and educators at every level. Use our interactive calculators alongside this curriculum guide to verify your calculations and explore concepts hands-on — no sign-up, no downloads, no limits.
Explore with SolveCalc's Math Tools Library→Frequently Asked Questions
What is 1/3 as a decimal? +
1/3 = 0.33333... (0.3 repeating). It is a repeating decimal because 3 is not a factor of 2 or 5.
Is 0.75 a terminating decimal? +
Yes. 0.75 = 75/100 = 3/4. It terminates because the denominator 4 = 2² has only 2 as a prime factor.
What is 6/7 as a decimal? +
6/7 = 0.857142857142... — a 6-digit repeating decimal. As a percentage it is approximately 85.71%.