Question

with the long division state whether the following will have the terminating of or non terminating repeating decimal expression 17 / 147 and 21/64 and 16/125 and 42/400

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Answer 1

Answer:

MATHS

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:

(i)

3125

13

(ii)

8

17

(iii)

455

64

(iv)

1600

15

(v)

343

29

(vi)

2

3

5

2

23

(vii)

2

2

5

7

7

5

129

(viii)

15

6

(ix)

50

35

(x)

210

77

October 15, 2019avatar

Veda Kesarwani

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VIDEO EXPLANATION

ANSWER

Theorem: Let x=

q

p

be a rational number, such that the prime factorisation of q is of the form 2

n

5

m

, where n, m are non-negative integers. Then, x has a decimal expansion which terminates.

(i)

3125

13

Factorise the denominator, we get

3125=5×5×5×5×5=5

5

So, denominator is in form of 5

m

so,

3125

13

is terminating.

Step-by-step explanation:

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