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Express the Following Decimal in the Form `P/Q`: `4.Bar7` - Mathematics

Question

Express the following decimal in the form `p/q`: `4.bar7`

Solution

Let `x=4.bar7`

`x=4+0.bar7`

Let `y = 0.bar7=0.777...`

⇒ 10y = 7.777...

⇒ 10y = 7 + 0.777...

⇒ 10y = 7 + y

⇒ 10y - y = 7

⇒ 9y = 7

⇒ y = 7/9

`therefore0.bar7=7/9`

Therefore,

`x=4+7/9`

`x=(36+7)/9`

`x=43/9`

Hence, `4.bar7=43/9`

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APPEARS IN

 RD Sharma Solution for Mathematics for Class 9 (2018 (Latest))
Chapter 1: Number Systems
1.3 | Q: 2.6 | Page no. 22
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Express the Following Decimal in the Form `P/Q`: `4.Bar7` Concept: Introduction of Real Number.
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