Question

Without actually performing division, state whether the following rational numbers will have a terminating decimal form or a non-terminating, repeating decimal form.
(i) 13/3125 (ii) 11/12 (iii) 64/455 (iv) 15/1600 (v) 29/343
(vi) 23/2³5² (vii) 2²7⁷5⁵/129 (viii) 9/15 (ix) 36/100 (x) 77 /210

Answer 1

Step-by-step explanation:

i hope ot will help full to all

Answer 2

Answer:

i) 13/3125(iv) 15/1600(vi) 23/2³5²(ix) 36/100 have a terminating decimal form

(ii) 11/12(iii) 64/455 (v) 29/343 (vii) 2²7⁷5⁵/129(viii) 9/15 (x) 77 /210 have a  non-terminating, repeating decimal form.

Step-by-step explanation:

If the denominator is in the form of 2ⁿ5ˣ. Then the rational numbers will have a terminating decimal form or else they have a non-terminating, repeating decimal form.

i) 13/3125

=13/5*5*5*5*5

= 13/5⁵

The denominator should be in form 2ⁿ5ˣ.

here denominator can be written as 5⁵*2⁰ where 2⁰ = 1,

= 13/5⁵*2⁰

here the denominator is in the form of 5⁵*2⁰

∴ 13/3125 has a terminating decimal form.

ii)11/12

= 11/2*2*3

= 11/2²×3

here denominator is not in form 2ⁿ5ˣ.

therefore 11/12 has a non-terminating decimal.

(iii) 64/455

= 64/5∗7∗13

here denominator is not in form 2ⁿ5ˣ.

64/455 has​ a non-terminating, repeating decimal.

(iv) 15/1600

= 15/2*2*2*2*2*2*5*5

= 15/2⁶5²

here denominator is in form 2ⁿ5ˣ.

15/1600 has a terminating decimal form.

v) 29/343

= 29/7*7*7

=29/7³

here denominator is not in form 2ⁿ5ˣ.

therefore 29/343 has a non-terminating, repeating decimal form.

(vi) 23/2³5²

here denominator is in form 2ⁿ5ˣ.

23/2³5² has a terminating decimal form.

(vii) 2²7⁷5⁵/129

here denominator cannot be written in the form of 2ⁿ5ˣ.

therefore  2²7⁷5⁵/129  has a non-terminating, repeating decimal form.

(viii) 9/15

here denominator cannot be written in the form of 2ⁿ5ˣ.

therefore 9/15  has a non-terminating, repeating decimal form.

(ix) 36/100

=  36/2*2*5*5

= 0.36

36/100 has a terminating decimal form.

(x) 77 /210

= 77 /3*7*5*2

here denominator cannot be written in the form of 2ⁿ5ˣ.

therefore 77 /210 has a non-terminating, repeating decimal form.

Click the below link for examples of recurring decimals and Fractions.

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