Evaluate the following repeating decimal

3.54

Evaluate the repeated piece

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

Subtract equations

Therefore, we have 100x - x = 354.54 - 3.54

99x = 351

Divide each side by 99

99x
99
=
  
351
99

x  =  351
  99

Simplify using a GCF of 9

351/9
99/9

Final Answer


39/11


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What is the Answer?
39/11
How does the Repeating Decimal Calculator work?
Free Repeating Decimal Calculator - 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
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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