Question

Convert 0.533333... to a fraction.
(only the 3 is repeating)

Please show the work!!

Answer 1

Let x = 0.5333333333 ...

So 100x = 53.3333333333 ...
and 10x = 5.3333333333 ...
---------------------------------
90x = 53 – 5 = 48.

So x = 48/90 = 8/15 after reduction to lowest terms (by factor of 6)
0.3333... = ⅓. and that 0.5 = ½.

So 0.533333... = 0.5 + 0.0333333...0.5 + 0.3333.../10 = 1/2 + (1/3)/10 = 1/2 + 1/30 = 16/30 = 8/15

Answer 2

The fractional form of the given repeating decimal number 0.533333... is $\frac{8}{15}$.

How to convert a repeating decimal number into a fraction?

We follow the some steps to convert the repeating decimal number into a fraction

Step1: Form an equation by setting the repeating decimal equal to x.

Step2: Multiply both the sides of the equation by multiples of 10 until just the repeating digits are to the right of the decimal.

Step3: Form another equation by multiplying both sides of the equation from step1 by multiples of 10 so that one set of the repeating digit or digits are to the left of the decimal.

Step4: Subtract the equation from step2 from the equation from step 3.

According to the given question.

We have a repeating decimal number 0.5333.

To convert the above repeating decimal number into a fraction we will do some following step:

Step1: Form an equation by setting the repeating decimal equal to x.

Let,

$x = 0.53333...$

$\implies x = 0.5\bar 3$

Step2: Multiply both the sides of the equation by multiples of 10 until just the repeating digits are to the right of the decimal.

$10x = 5.\bar 3$

Step3: Form another equation by multiplying both sides of the equation from step1 by multiples of 10 so that one set of the repeating digit or digits are to the left of the decimal.

$100x = 53.\bar3$

Step4: Subtract the equation from step2 from the equation from step 3.

$100x -10x = 53.\bar3-5.\bar3$

$\implies 90x = 48$

Step5: Solve for x.

$90x = 48$

$\implies x = \frac{48}{90}$

$\implies x = \frac{24}{45}$

$\implies x = \frac{8}{15}$

Hence, the fractional form of the given repeating decimal number 0.533333... is $\frac{8}{15}$.

Find out more information about how to convert a repeating decimal number into a fraction here:

https://brainly.com/question/11050898

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