Question

Rewrite as a simplified fraction. 2.31 with the 1 repeating

Answer 1

Answer: $\frac{104}{45}$

Step-by-step explanation:

$2.31^-$

Let x be equal to that.

$x=2.31^-$

Multiply by 1 followed by as many zeros as repeating numbers. In this case it's just one repeating decimal, therefore, 1 followed by 1 zero or 10.

$10x=2.31^-*10$

This basically moves the decimal point one number to the right.

$10x=23.11^-$

Subtract the first equation from this new equation.

$10x=23.11^-\\-x=2.31^-$

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The repeating decimal is eliminated and we are left with:

23.1

- 2.3

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20.8

We also have 10 - 1 = 9. We are left with:

$9x=20.8$

Divide by 9.

$x=\frac{20.8}{9}$

To get rid of the decimal, multiply by 1 followed by as many zeros as decimals. In this case 1.

$x=\frac{20.8}{9} (\frac{10}{10} )$

$x=\frac{208}{90}$

Let's simplify.

208/2=104

90/2=45

$x=\frac{104}{45}$