हिंदी

Express the following recurring decimal as a rational number: 51.02¯

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प्रश्न

Express the following recurring decimal as a rational number:

`51.0bar(2)`

योग
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उत्तर

`51.0bar(2)` = 51 + 0.02 + 0.002 + 0.0002 + ...    ...(1)

These terms after the first term form a G.P. whose first term is a = 0.02 and common ratio = r = 0.1

Since |r| = |0.1| = 0.1 < 1, the sum to infinity of this G.P. exists and

S = `"a"/(1 - "r")`

= `0.02/(1 - 0.1)`

= `0.02/0.9`

= `2/90`

= `1/45`

∴ from (1), `51.0bar(2) = 51 + 1/45`

= `(2295 + 1)/45`

= `2296/45`

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अध्याय 2: Sequences and Series - Exercise 2.3 [पृष्ठ ३३]

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बालभारती Mathematics and Statistics (Arts and Science) Part 2 [English] Standard 11 Maharashtra State Board
अध्याय 2 Sequences and Series
Exercise 2.3 | Q 2. (iv) | पृष्ठ ३३

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