Sunday, 13 September 2015

DECIMAL TO FRACTION CONVERTER



Decimal to Fraction Conversion

Decimal to fraction conversion calculator

Enter a decimal number and press the Convert button:
Fraction result:
Calculation:

How to convert decimal to fraction

Example: convert 2.56 to fraction:
2.56 = 2+56/100
gcd(56,100) = 4
2+56/100 = 2+(56/4)/(100/4) = 2+14/25

  1. Count the number of digits (d) to the right of the decimal point of the decimal number x.Example: 2.56 has 2 digits to the right of the decimal point, so d=2.
  2. Calculate the factor (f) for making the decimal number an integer:
    f = 10d
    Example:
    f = 102 = 100
  3. Multiply and divide the decimal number x by the factor f:
    x × f / f  =  y / f
    Example:
    2.56 × 100 / 100 = 256 / 100
    4. Example:
    gcd(256,100) = 4

  • Reduce the fraction by dividing the numerator and denominator by the gcd value:Example:
    256 / 100 = (256/4) / (100/4) = 64/25

    • How to convert repeating decimal to fraction

    Example #1

    Convert 0.333333... to fraction:
    x = 0.333333...
    10x = 3.333333...
    10x - x = 9x = 3
    x = 3/9 = 1/3

    Example #2

    Convert 0.0565656... to fraction:
    x = 0.0565656...
    100x = 5.6565656...
    100x - x = 99x = 5.6
    990x = 56
    x = 56/990 = 28/495

    Decimal to fraction conversion table

    Decimal Fraction
    0.01000000 1/100
    0.10000000 1/10
    0.11111111 1/9
    0.12500000 1/8
    0.14285714 1/7
    0.16666667 1/6
    0.20000000 1/5
    0.22222222 2/9
    0.25000000 1/4
    0.28571429 2/7
    0.30000000 3/10
    0.33333333 1/3
    0.37500000 3/8
    0.40000000 2/5
    0.42857143 3/7
    0.44444444 4/9
    0.50000000 1/2
    0.55555555 5/9
    0.57142858 4/7
    0.62500000 5/8
    0.66666667 2/3
    0.60000000 3/5
    0.70000000 7/10
    0.71428571 5/7
    0.75000000 3/4
    0.77777778 7/9
    0.80000000 4/5
    0.83333333 5/6
    0.85714286 6/7
    0.87500000 7/8
    0.88888889 8/9
    0.90000000 9/10


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