Advertisements
Advertisements
Question
Express the following recurring decimal as a rational number:
`0.bar32`
Advertisements
Solution
`0.bar32` = 0.323232…
= 0.32 + 0.0032 + 0.000032 + …
Here, 0.32, 0.0032, 0.000032, … are in G.P. with a = 0.32 and r = 0.01
Since, |r| = |0.01| < 1
∴ Sum to infinity exists.
∴ Sum to infinity = `a/(1 - r)`
∴ `0.bar32` = `0.32/(1 - (0.01)) = 0.32/0.99`
∴ `0.bar32 = 32/99`
APPEARS IN
RELATED QUESTIONS
Express the following recurring decimal as a rational number:
`3.dot5`
Express the following recurring decimals as a rational number:
`0.3bar45`
If the first term of a G.P. is 16 and sum of its terms to infinity is `176/5`, find the common ratio.
Express the following recurring decimals as a rational number.
`3.dot5`
Express the following recurring decimals as a rational number.
`3.dot5`
Express the following recurring decimal as a rational number.
\[\ce{3.\overset{.}{5}}\]
Express the following recurring decimals as a rational number.
`0.3bar45`
Express the following recurring decimal as a rational number.
`3.4 bar 56`
Express the following recurring decimal as a rational number.
`3.dot5`
Express the following recurring decimal as a rational number.
`3.dot5`
Express the following recurring decimal as a rational number.
`3.4bar56`
Express the following recurring decimal as a rational number.
`3.4bar56`
Express the following recurring decimal as a rational number.
`3.dot5`
Express the following recurring decimal as a rational number.
`3.4bar(56)`
