This is a repeating decimal which can be written as 4.
57, and there is a special formula to determine the fraction
The repeated piece 57 has a length of 2
Therefore, we setup two equations.
Equation 1: x = 4.57
Equation 2: 100x = 10
2 100x 4.57 → 100x = 100 x 4.57 → 100x = 457
Therefore, we have 100x - x = 457 - 4.57
99x = 457
Divide each side of the equation by 99
How does the Repeating Decimal Calculator work?
Evaluates and simplifies a repeating decimal
This calculator has 2 inputs.
What 3 formulas are used for the Repeating Decimal Calculator?
- For a number n, calculate number of decimal places to the right of the decimal, call this d
-
Setup an equation where 10dx - x = n * 10d
- Isolate x to determine the fraction
For more math formulas, check out our
Formula Dossier
What 7 concepts are covered in the Repeating Decimal Calculator?
- decimal
- Number in the form a/b where the result is not a whole number
- denominator
- The bottom portion of a fraction. For a/b, b is the denominator
- equation
- a statement declaring two mathematical expressions are equal
- fraction
- how many parts of a certain size exist
a/b where a is the numerator and b is the denominator - number
- an arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations and for showing order in a series or for identification. A quantity or amount.
- numerator
- the number above the line in a common fraction
- repeating decimal
- a decimal fraction in which a figure or group of figures is repeated indefinitely, as in 0.1111
Example calculations for the Repeating Decimal Calculator
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