Turn a decimal into a fraction in its simplest form.
The decimal is multiplied by a power of ten large enough to make it a whole number.
That becomes the numerator, and the power of ten becomes the denominator.
Both are divided by their greatest common divisor to reduce the fraction.
Fraction: Decimal × 10ⁿ ÷ 10ⁿ
n: Number of decimal places
Then: Divide both parts by their GCD
Converting 0.75 into a fraction.
Decimal: 0.75
Two decimal places, so multiply by 100: 0.75 × 100 = 75
Write as a fraction: 75/100
Divide both by their GCD of 25: 3/4
Answer: 3/4
A decimal to fraction calculator rewrites a decimal number such as 0.625 as an exact fraction in its simplest form, here 5/8. It is the tool for turning a reading from a digital display, a measurement or a bank rate into a fraction you can work with by hand.
Students need this conversion when a question asks for an answer 'in the form p/q', when rationalising results in algebra, or when comparing decimals and fractions in Class 7 and 8. Carpenters and tailors who work in inches meet it when a tape reads 0.375 and they need the nearest eighth. The calculator also shows the mixed-number form for values above 1, so 1.375 appears as 1 3/8.
1. Count the number of digits after the decimal point, n.
2. Remove the decimal point to get a whole number N. For example, 0.625 gives N = 625 with n = 3.
3. Write the fraction N ÷ 10ⁿ, here 625/1000.
4. Find the HCF of N and 10ⁿ.
5. Divide both by the HCF to reach lowest terms.
6. If the fraction is improper, you may also write it as a mixed number.
Our place-value system is built on tenths, hundredths and thousandths. The digit in the third decimal place counts thousandths, so a decimal with three places is simply a count of thousandths. 0.625 is 625 thousandths, which is 625/1000 by definition. No approximation is involved. Simplifying then removes the shared factors. Since 1000 = 2³ × 5³, the only factors that can cancel are 2s and 5s, which is why a terminating decimal always simplifies to a denominator made only of 2s and 5s.
A decimal that ends converts exactly with this method. A repeating decimal such as 0.333... needs algebra instead: let x = 0.333..., then 10x = 3.333..., subtract to get 9x = 3, so x = 1/3. This calculator cannot see an infinite repeat, because a computer stores 0.333... as a finite rounded value. It converts what it is given, up to 10 decimal places, so a typed repeating decimal gives a fraction close to, but not exactly, the intended one. For those, enter the fraction directly.
Numbers such as √2 and π have decimals that neither end nor repeat. No fraction p/q equals them exactly, which is what 'irrational' means. Familiar approximations like 22/7 for π are useful but not equal. If you type 3.14159, the calculator returns 314159/100000, which is exactly 3.14159 and not π. Knowing the difference matters in Class 9 when proving numbers irrational, and in exams where an answer 'in terms of π' is expected.
Irfan's digital kitchen scale shows 0.625 kg of paneer, and his mother's recipe card lists quantities as fractions of a kilogram.
Answer: Fraction 5/8; Check 0.625
Writing 0.625 as 625/100 by using one power of ten too few.
Stopping at 625/1000 without reducing to lowest terms.
Typing a rounded repeating decimal like 0.33 and expecting 1/3; it gives 33/100.
Treating 22/7 as the exact value of π in a question that asks for an exact answer.
Answering 'express in the form p/q' questions in Class 9 number systems.
Converting digital measurements into inch fractions for carpentry, tailoring or hardware sizes.
Turning decimal probabilities into fractions for probability chapters.
Rewriting decimal quantities in recipes that use half, quarter and eighth measures.
Can every decimal be written as a fraction?
Every decimal that ends, or repeats, can be. Numbers like π and √2 never end or repeat, so they cannot be written exactly as a fraction.
How accurate is the conversion for a repeating decimal?
Very close, but not exact. A computer stores 0.333… as a rounded value, so the conversion is based on that rounded number. For exact work, enter the fraction directly instead.