# Express the following recurring decimals as a rational number : 3.5. - Mathematics and Statistics

Sum

Express the following recurring decimals as a rational number:

3.dot5

#### Solution

3.dot5 = 3.555… = 3 + 0.5 + 0.05 + 0.005 + …

Here, 0.5, 0.05, 0.005, … are in G.P. with
a = 0.5 and r = 0.1.

Since, | r | = |0.1| < 1

∴ Sum to infinity exists.

∴ Sum to infinity = "a"/(1 - "r") = 0.5/(1 - (0.1)) = 0.5/0.9 = 5/9

∴ 3.dot5 = 3 + 5/9 = 32/9.

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. (ii) | Page 57