Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a nonterminating repeating decimal expansion: (i) 13/3125 (ii) 17/8 (iii) 64/455
Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a nonterminating repeating decimal expansion:
(i) 13/3125
(ii) 17/8
(iii) 64/455
(iv) 15/1600
(v) 29/343
(i) 13/3125
Factorizing the denominator, we get,
3125 = 5 × 5 × 5 = 5^{5}
Since, the denominator has only 5 as its factor, 13/3125 has a terminating decimal expansion.
(ii) 17/8
Factorizing the denominator, we get,
8 = 2×2×2 = 2^{3}
Since, the denominator has only 2 as its factor, 17/8 has a terminating decimal expansion.
(iii) 64/455
Factorizing the denominator, we get,
455 = 5×7×13
Since, the denominator is not in the form of 2^{m} × 5^{n}, thus 64/455 has a nonterminating decimal expansion.
(iv) 15/ 1600
Factorizing the denominator, we get,
1600 = 2^{6}5^{2}
Since, the denominator is in the form of 2^{m} × 5^{n}, thus 15/1600 has a terminating decimal expansion.
(v) 29/343
Factorizing the denominator, we get,
343 = 7×7×7 = 7^{3} Since, the denominator is not in the form of 2^{m} × 5^{n} thus 29/343 has a nonterminating decimal expansion.

The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form, p q what can you say about the prime factors of q? (i) 43.123456789 (ii) 0.120120012000...
1 year ago

Without actually performing the long division, state whether the following rational numbers (i) 23/(2^35^2) (ii) 129/(2^25^77^5) (iii) 6/15 (iv) 35/50
1 year ago

Prove that the following are irrationals: (i) 1/√2 (ii) 7√5 (iii) 6 + √2
1 year ago

Prove that 3 + 2√5 is irrational.
1 year ago

Prove that √5 is irrational.
1 year ago
Latest Post: Assertion: Excess of nitrates in drinking water are harmful for infants. Our newest member: casinoen32917304 Recent Posts Unread Posts Tags
Forum Icons: Forum contains no unread posts Forum contains unread posts
Topic Icons: Not Replied Replied Active Hot Sticky Unapproved Solved Private Closed
Super Globals
Requests: Array ( )
Server: Array ( )