Question

What is 3.53 with the 3 repeating as a fraction

Answer 1

Answer:

$\frac{53}{15}$

Step-by-step explanation:

We require to create 2 equations with the repeating value after the decimal point.

let x = 3.533333... ← multiply both sides by 10 then by 100

10x = 35.3333... → (1)

100x = 353.3333... → (2)

Subtract (1) from (2) thus eliminating the repeating value

90x = 318 ( divide both sides by 90 )

x = $\frac{318}{90}$ = $\frac{53}{15}$

Answer 2

To find the fraction with 3 repeating, we have to create equation with repeating value of fraction.

The fraction would be $\dfrac{53}{15}$.

Given:

The given number is 3.53.

Let fraction is $x$.

Write the repeating value of fraction.

$x=3.53333$

Multiply both by side 10.

$10x=10\times 3.5333$----------------------- (1)

Multiply both side by 100.

$100x=100\times 3.5333$-------------------(2)

Subtract equation (1) and (2).

$90x = 318\\x=\dfrac{318}{90}\\x=\dfrac{53}{15}$

Thus, the fraction would be $\dfrac{53}{15}$.

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