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  • 02-04-2019
  • Mathematics
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(2CQ) Write the repeating decimal as a fraction .15

2CQ Write the repeating decimal as a fraction 15 class=

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kudzordzifrancis
kudzordzifrancis kudzordzifrancis
  • 02-04-2019

Answer:

c. [tex]\frac{5}{33}[/tex]

Step-by-step explanation:

The given decimal is  [tex]0.\bar {15}[/tex]

Let  [tex]y=0.\bar {15}...(1)[/tex]

Multiply equation (1) by 100.

[tex]100y=15.\bar {15}...(2)[/tex]

Subtract equation (1) from equation (2)

[tex]\Rightarrow 100y-y=15.\bar {15}-0.\bar {15}[/tex]

[tex]\Rightarrow 99y=15[/tex]

Divide both sides by 99.

[tex]\Rightarrow y=\frac{15}{99}[/tex]

Simplify;

[tex]\Rightarrow y=\frac{5}{33}[/tex]

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