Write down the decimal expansions of these rational numbers which have terminating decimal expansions.
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Answers
Answer:
Step-by-step explanation:
(i) 13/3125
it is in the form of 2ⁿ5ⁿ ∴ it is terminating.
it's decimal expansion is
13 × 2⁵/5⁵ × 2⁵
= 416/100000
= 0.00416
(ii) 17/8
it is in the form of 2ⁿ5ⁿ ∴ it is terminating.
17 × 5³/2³ × 5³
= 2125/1000
= 2.125
(iii) 64/455
it is not in the form of 2ⁿ5ⁿ ∴ it is non terminating.
(iv) 15/1600
it is in the form of 2ⁿ5ⁿ ∴ it is terminating.
15 × 5⁴/2⁶ × 5² × 5⁴
= 9375/1000000
= 0.009375
(v) 29/343
it is not in the form of 2ⁿ5ⁿ ∴ it is non terminating.
(vi) 23/5³2²
it is in the form of 2ⁿ5ⁿ ∴ it is terminating.
= 23 × 2/5³ × 2³
= 46/1000
= 0.046
(vii) 129/²5⁷7⁵
it is not in the form of 2ⁿ5ⁿ ∴ it is non terminating.
(viii) 6/15
it is not in the form of 2ⁿ5ⁿ. but the numerator and the denominator are divisible.
∴ it is terminating.
6/15 = 2/5
= 0.4
(ix) 35/50
it is in the form of 2ⁿ5ⁿ. ∴ it is terminating.
= 35 × 2/50 × 2
= 70/100
= 0.7
(x) 77/210
it is not in the in the form of 2ⁿ5ⁿ ∴ it is non terminating.
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