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Express the following recurring decimals as a rational number: 3.456¯ - Mathematics and Statistics

Sum

Express the following recurring decimals as a rational number: `3.4bar56`

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Solution

`3.4bar56` = 3.4565656 …
= 3.4 + 0.056 + 0.00056 + 0.0000056 + ….
Here, 0.056, 0.00056, 0.0000056, … are in
G.P. with a = 0.056 and r = 0.01
Since, | r| = |0.01| < 1
∴ Sum to infinity exists.

∴ Sum to infinity = `"a"/(1 - "r")`

= `0.056/(1 - 0.01)`

= `0.056/0.99`

= `56/990`

∴ `3.4bar56 = 3.4 + 56/990` 

= `34/10 + 56/990`

= `(3366 + 56)/990`

= `3422/990`

= `1711/495`.

Concept: Recurring Decimals
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 4 Sequences and Series
Exercise 4.3 | Q 2. (v) | Page 57
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