Advertisements
Advertisements
प्रश्न
Has the rational number \[\frac{441}{2^2 \times 5^7 \times 7^2}\] a terminating or a nonterminating decimal representation?
उत्तर
We have,
`441/(2^2xx5^7xx7^2)`
Theorem states:
Let `x=p/q` be a rational number, such that the prime factorization of q is not of the form `2^nxx5^m` , where mand n are non-negative integers.
Then, x has a decimal expression which is non-terminating repeating.
This is clear that the prime factorization of the denominator is not of the form `2^nxx5^m` .
Hence, it has non-terminating decimal representation.
APPEARS IN
संबंधित प्रश्न
State Euclid's division lemma.
Write 98 as product of its prime factors.
Write the condition to be satisfied by q so that a rational number\[\frac{p}{q}\]has a terminating decimal expansion.
What is an algorithm?
What is a lemma?
State whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
`29/343`
State whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
`77/210`
Write down the decimal expansion of the following number which have terminating decimal expansion.
`64/455`
Write the denominator of the rational number `257/5000` in the form 2m × 5n, where m, n are non-negative integers. Hence, write its decimal expansion, without actual division.
The following real number have decimal expansions as given below. In the following case, decide whether it is rational or not. If it is rational, and of the form p/q what can you say about the prime factors of q?
0.120120012000120000. . .
