How to Convert Fractions to Decimals (and Back Again)

Fractions and decimals are two ways to write the same number — and once you can flip between them in seconds, ratios, percents, and word problems all get easier. Here’s a clean, no-nonsense way to learn it.

This guide covers every direction you can convert: fraction to decimal, terminating decimal back to a fraction, repeating decimal to a fraction (the algebra trick), and decimal to percent. Whatever your test asks for, you’ll be ready.

Fraction → decimal: just divide

A fraction is a division statement. The top number goes inside the long-division box; the bottom number goes outside.

• $\tfrac{3}{4} = 3 \div 4 = 0.75$.
• $\tfrac{7}{8} = 7 \div 8 = 0.875$.
• $\tfrac{1}{3} = 1 \div 3 = 0.3333\ldots = 0.\overline{3}$ (the bar means it repeats).

Some fractions give clean terminating decimals (they end). Others give repeating decimals. The pattern: if the bottom of the simplified fraction has only 2s and 5s as factors, it terminates. Otherwise, it repeats.

Why this rule works. Decimal notation is base-10. The denominators of all terminating decimals must therefore be made up of the prime factors of 10: namely, 2 and 5. Any other prime factor in the denominator forces a repeating tail.

Decimal → fraction: count the places

Look at how many digits are after the decimal point.

• One digit → over 10.
• Two digits → over 100.
• Three digits → over 1000.

Then simplify.

• $0.6 = \tfrac{6}{10} = \tfrac{3}{5}$.
• $0.25 = \tfrac{25}{100} = \tfrac{1}{4}$.
• $0.375 = \tfrac{375}{1000} = \tfrac{3}{8}$.

With whole-number parts. $2.75 = 2 + \tfrac{75}{100} = 2\tfrac{3}{4} = \tfrac{11}{4}$.

Repeating decimal → fraction (the algebra trick)

To turn $0.\overline{6}$ into a fraction:

1. Let $x = 0.6666\ldots$.
2. Multiply by 10: $10x = 6.6666\ldots$.
3. Subtract: $10x – x = 6 \to 9x = 6 \to x = \tfrac{6}{9} = \tfrac{2}{3}$.

For a two-digit repeat like $0.\overline{27}$, multiply by 100 instead.

Two-digit example. Convert $0.\overline{27}$.

• $x = 0.272727\ldots$.
• $100x = 27.272727\ldots$.
• $100x – x = 27 \to 99x = 27 \to x = \tfrac{27}{99} = \tfrac{3}{11}$.

Mixed (partly repeating) example. Convert $0.1\overline{6}$ (the 6 repeats but the 1 does not).

• $x = 0.1666\ldots$, so $10x = 1.666\ldots$.
• $100x = 16.666\ldots$.
• Subtract: $90x = 15 \to x = \tfrac{15}{90} = \tfrac{1}{6}$.

Five conversions worth memorizing

These five power through 80% of test problems.

Bonus table — fractions with denominators of 8 and 16

These are common on SAT/ACT problems involving measurements.

Knowing 1/8 = 0.125 unlocks all of these instantly — just add 0.125 each step.

Common mistakes

• Forgetting to simplify after converting decimals → fractions.
• Reading $0.\overline{3}$ as “exactly 0.3” — they’re different numbers.
• Dividing in the wrong direction (always top ÷ bottom).
• Mis-counting the number of decimal places when converting to a fraction.
• Treating $0.999\ldots$ as less than 1 — it actually equals 1.

Quick practice

1. Convert $\tfrac{5}{8}$ to a decimal. Answer: 0.625.
2. Convert 0.04 to a fraction. Answer: $\tfrac{1}{25}$.
3. Convert $0.\overline{45}$ to a fraction. Answer: $\tfrac{5}{11}$.
4. Will $\tfrac{7}{40}$ terminate? Answer: Yes — 40 = $2^3 \cdot 5$, only 2s and 5s.
5. Convert $\tfrac{11}{20}$ to a decimal. Answer: 0.55.
6. Convert $0.0\overline{6}$ to a fraction. Answer: $\tfrac{1}{15}$.
7. Will $\tfrac{9}{15}$ terminate? Answer: Simplify first to $\tfrac{3}{5}$. Yes, terminates as 0.6.
8. Convert $\tfrac{17}{25}$ to a decimal. Answer: 0.68.

Connecting fractions, decimals, and percents

The three forms are interchangeable, and being able to flip between them instantly is one of the biggest test-day advantages you can build.

The most common SAT/ACT trick is mixing forms inside the same problem — for example, “What is 25% of $\tfrac{4}{5}$?” If you’re fluent in all three forms, you’d see this as $\tfrac{1}{4} \times \tfrac{4}{5} = \tfrac{1}{5} = 0.2 = 20\%$.

The clever 0.999… = 1 explanation

This surprises a lot of students: $0.\overline{9} = 1$ exactly. Here’s the proof using the algebra trick from earlier:

• Let $x = 0.999\ldots$.
• $10x = 9.999\ldots$.
• Subtract: $9x = 9 \to x = 1$.

It’s not “almost” 1. It is 1, written in a different form.

Working with negative fractions and decimals

The conversion rules don’t change for negatives — just keep the sign with the fraction throughout.

• $-\tfrac{3}{4} = -0.75$.
• $-0.625 = -\tfrac{5}{8}$.
• $-1\tfrac{1}{2} = -1.5 = -\tfrac{3}{2}$.

A common mistake: dropping the negative sign halfway through a multi-step conversion. Anchor the sign at the start and don’t lose track of it.

Why this skill matters

Fluency between fractions and decimals is foundational for:

• Probability (often written as fractions, but tested as decimals or percents).
• Financial math (interest rates, sales tax, discounts).
• Statistics (data is often in decimals; ratios in fractions).
• Measurement (rulers use fractions; metric uses decimals).
• All standardized tests — the SAT explicitly mixes forms in the answer choices.

FAQ

What’s the easiest way to convert a fraction to a decimal?

Long division: top divided by bottom.

How do I know if a fraction will give a terminating decimal?

Simplify it first. If the denominator factors into only 2s and 5s, it terminates.

How do I turn a repeating decimal into a fraction?

Use the algebra trick above — set the decimal equal to $x$, multiply to shift the repeat, and subtract.

Can every decimal be written as a fraction?

Every rational decimal — yes. Irrational decimals (like $\pi$ or $\sqrt{2}$) cannot.

Are fraction-to-decimal conversions on standardized tests?

Absolutely. The SAT, ACT, GED, and TEAS all rely on you being fluent here.

How do I convert a fraction to a percent?

Convert the fraction to a decimal, then multiply by 100. $\tfrac{3}{8} = 0.375 = 37.5\%$.

What if my decimal is mixed (some repeating, some not)?

Use the algebra trick, but multiply by powers of 10 to shift both the non-repeating and repeating parts.

Are repeating decimals considered rational?

Yes. Every repeating decimal is a ratio of two integers, so it’s rational.

How do I know if a fraction will give a terminating or repeating decimal?

Reduce the fraction first. If the simplified denominator’s only prime factors are 2 and/or 5, the decimal terminates. Anything else — 3, 7, 11, 13 — and the decimal will repeat. Example: $\tfrac{7}{40}$ terminates because $40 = 2^3 \cdot 5$. But $\tfrac{5}{12}$ repeats because $12 = 2^2 \cdot 3$.

Are irrational numbers also decimals?

Yes — they’re decimals that never terminate and never repeat. Famous examples: $\pi \approx 3.14159\ldots$, $\sqrt{2} \approx 1.41421\ldots$, and $e \approx 2.71828\ldots$. They can be written as decimals but never as exact fractions.

Why do bankers and scientists prefer decimals over fractions?

Decimals plug straight into calculators, line up neatly in columns, and are easier to compare at a glance. A scientist who writes “0.0042” can immediately tell it’s smaller than “0.0067.” Comparing $\tfrac{42}{10000}$ to $\tfrac{67}{10000}$ is just as easy — once you reduce them — but takes more steps.

Is 0.5 a fraction or a decimal?

It’s a decimal. But it’s exactly equal to the fraction $\tfrac{1}{2}$. Numbers don’t “belong” to one form — they just have multiple equivalent representations.

How do I convert a mixed number to a decimal?

Keep the whole part. Convert the fractional part to a decimal. Add them. $3\tfrac{1}{4} = 3 + 0.25 = 3.25$.

Speed-conversion table to memorize

Know these 8 cold and you’ll solve half the SAT percent/fraction problems on sight — no scratchwork needed.

One last reminder

Progress in math compounds. A 1% improvement every day for 100 days yields nearly a 3x improvement overall, because each new concept builds on the last. The students who pull ahead aren’t the ones who study the longest — they’re the ones who study consistently, review their mistakes, and refuse to skip the foundations. Show up tomorrow. Then show up the day after. The results take care of themselves.

If you found something useful here, save this article and revisit it after your next practice session. You’ll catch nuances on the second read that you missed on the first, because by then you’ll have the experience to recognize them. Happy practicing.

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