# 3.54repeating repeating decimal

## Enter Repeating Decimal

This is a repeating decimal which can be written as 3.54, and there is a special formula to determine the fraction
The repeated piece 54 has a length of 2
Therefore, we setup two equations.
Equation 1: x = 3.54
Equation 2: 100x = 102 100x 3.54 → 100x = 100 x 3.54 → 100x = 354
Therefore, we have 100x - x = 354 - 3.54
99x = 354

## Divide each side of the equation by 99

 99x 99
 =
 354 99

 x  = 354 99

354/99

### 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?

1. For a number n, calculate number of decimal places to the right of the decimal, call this d
2. Setup an equation where 10dx - x = n * 10d
3. 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