Advertisements
Advertisements
Question
Express 0.`bar(4)` as a rational number simplest form.
Solution
Let x be 0.`bar(4)`
x = 0.`bar(4)` ….(1)
Multiplying both sides by 10, we get
10x = 4..`bar(4)`….(2)
Subtracting (1) from (2), we get
10x – x = 4..`bar(4)` - 0..`bar(4)`
⇒9x = 4
⇒x = 49
Thus, simplest form of 0..`bar(4)` as a rational number is `4/9`.
APPEARS IN
RELATED QUESTIONS
Write the decimal expansion of `73/ ((2^4×5^3))`
Without actually performing the long division, state whether state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
Without actually performing the long division, state whether state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
What is a lemma?
State whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
`64/455`
State whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
`129/(2^2xx5^7xx7^5)`
State whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
`35/50`
Write down the decimal expansion of the following number which have terminating decimal expansion.
`13/3125`
The decimal expansion of the rational number `97/(2 xx 5^4)` will terminate after ______.
A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q, when this number is expressed in the form `p/q`? Given reasons.
