Question

1. Without actually performing the long division, state whether the following numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:(I)15/1600 (II)29/343 (III)23/2 to the power 3 multiply by 5 to the power 2 (IV)129/2 to the power 2 multiply by 5 to the power 7 multiply by 7 to the power 5 (V)35/50 (VI)77/210
please help​

Answer 1

Answer:

do prime factorization and if the digits have only the powers of 2 and 5 or 2 only or 5 only then it is terminating

Answer 2

Hey mate,

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Here is your solution,

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●(i)

q = 320 = =

Here, denominator is of the form , where m = 1 and n = 6.

It means rational number  has a terminating decimal expansion.

(ii)

q = 343 =

Here, denominator is not of the form , where m and n are non-negative integers.

It means rational number  has non-terminating repeating decimal expansion.

(iii)

q =

Here, denominator is of the form , where m = 2 and n = 3 are non-negative integers.

It means rational number  has terminating decimal expansion.

(iv)

q =

Here, denominator is not of the form , where m and n are non-negative integers.

It means rational number  has non-terminating repeating decimal expansion.

(v)

Here, denominator is of the form , where m = 1 and n = 0.

It means rational number  has terminating decimal expansion.

(vi)

q = 10 =

Here, denominator is of the form , where m = 1 and n = 1.

It means rational number  has terminating decimal expansion.

(x)

Here, denominator is not of the form , where m and n are non-negative integers.

It means rational number  has non-terminating repeating decimal expansion.

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Hope this will help you,

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PHEONIX•Anku