Advertisements
Advertisements
Question
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.
Solution
327.7081 is terminating decimal number.
So, it represents a rational number and also its denominator must have the form 2m × 5n.
Thus, 327.7081 = `3277081/10000 = p/q`
∴ q = 104
= 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5
= 24 × 54
= (2 × 5)4
Hence, the prime factors of q is 2 and 5.
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.
What can you say about the prime factorisations of the denominators of the following rationals: 0.120120012000120000 ...
State Euclid's division lemma.
What is a lemma?
State whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
`15/1600`
Write down the decimal expansion of the following number which have terminating decimal expansion.
`13/3125`
Write down the decimal expansion of the following number which have terminating decimal expansion.
`29/343`
Write down the decimal expansion of the following number which have terminating decimal expansion.
`129/(2^2xx5^7xx7^5)`
The decimal expansion of the rational number `14587/1250` will terminate after ______.
