Decimal Fraction Conversion

This calculator converts decimal numbers to fractions and fractions to mixed numbers. For repeating decimals, enter the number of decimal places in the repeating sequence to get an accurate fraction conversion.

Decimal Fraction Conversion

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    Introduction

    What is a Decimal?

    In mathematics, a decimal is a number that uses a decimal point to separate the whole number part from the fractional part. The dot itself is called the decimal point. The digits to the right of the decimal point represent values less than one (such as tenths, hundredths, etc.), allowing for precise calculations beyond whole integers.

    What is a Fraction?

    A fraction represents a part of a whole. It consists of two specific numbers separated by a line:

    • Numerator (Top Number): Represents the number of parts you have.
    • Denominator (Bottom Number): Represents the total number of equal parts that make up the whole.

    How to Convert a Decimal to a Fraction

    Follow these simple steps to convert any decimal into a fraction:

    1. Create a Basic Fraction: Write the decimal number as the numerator (top) and 1 as the denominator (bottom).
      • Example: For 0.75, write 0.75 / 1.
    2. Remove the Decimal Point: Count how many digits are to the right of the decimal point. Multiply both the numerator and the denominator by 10 for every digit.
      • Example: 0.75 has 2 digits. Multiply by 100 (10210^2).
      • Result: 75 / 100.
    3. Simplify the Fraction: Find the Greatest Common Divisor (GCD) for both numbers and reduce the fraction to its lowest terms.
      • Example: The GCD of 75 and 100 is 25.
      • 75÷25=375 \div 25 = 3
      • 100÷25=4100 \div 25 = 4
      • Final Result: 3/4.
    4. Mixed Numbers: If the decimal is greater than 1 (e.g., 1.5), convert the result into a mixed number if necessary.

    Decimal to Fraction Conversion Table

    DecimalFractionDecimalFraction
    0.00011/100000.51/2
    0.0011/10000.555...5/9
    0.011/1000.57144/7
    0.08331/120.63/5
    0.09091/110.6255/8
    0.11/100.666...2/3
    0.111...1/90.77/10
    0.1251/80.71425/7
    0.14281/70.753/4
    0.166...1/60.777...7/9
    0.21/50.84/5
    0.222...2/90.833...5/6
    0.251/40.85716/7
    0.28572/70.8757/8
    0.33/100.888...8/9
    0.333...1/30.99/10
    0.3753/81.111/10
    0.42/51.255/4
    0.42853/71.53/2
    0.444...4/91.757/4

    Frequently Asked Questions

    What are the 3 types of decimals?

    (1) Terminating decimals: these have a finite number of digits after the decimal point. (2) Recurring decimals: these have one or more repeating numbers or sequences of numbers after the decimal point, which continue infinitely. (3) Decimals which go on for ever, never ending and never forming a repeating pattern. These numbers are called irrational numbers and cannot be expressed as a fraction. We cover these decimals in the number course.

    What is a non decimal number?

    The number of digits a numeric system uses is called its radix. ... However, for raw binary information, non-decimal numbers (especially hex) are much easier to work with, and they are universally used by programmers from the largest mainframe to the smallest microcomputer.

    Where is a decimal?

    The decimal point is placed in between the ones and the tenths. The whole number is written to the left of the decimal point. The fractional part is written to the right of the decimal point. The decimal point makes it easy to read a decimal number.

    What are the 3 types of fraction?

    In Maths, there are three major types of fractions. They are proper fractions, improper fractions and mixed fractions. Fractions are those terms which have numerator and denominator.

    How do you do fractions in math?

    Step 1: Make sure the bottom numbers (the denominators) are the same. Step 2: Add the top numbers (the numerators), put that answer over the denominator. Step 3: Simplify the fraction (if needed)

    What is the formula of fraction?

    Fraction = number of parts / total parts Every fraction has a numerator that equals the number of parts we have and a denominator equaling the total number of parts in a whole.

    What is a proper fraction?

    A fraction in which the numerator is less or of lower degree than the denominator.

    How do I turn a decimal into a fraction?

    To convert a decimal to a fraction, place the decimal number over its place value. For example, in 0.6, the six is in the tenths place, so we place 6 over 10 to create the equivalent fraction, 6/10. If needed, simplify the fraction.

    What is improper fraction example?

    A fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). Example: 5/3 (five thirds) and 9/8 (nine eighths) are improper fractions.

    What are the most common fractions?

    A fraction where both top and bottom numbers are integers. Example: 1/2 and 3/4 are both Common Fractions. But 1.2/4 is NOT a Common Fraction.

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