# 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

Is there an error in this question or solution?

#### APPEARS IN

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