Write down the decimal expansions of the number 29/343 terminating d

1.	Write down the decimal expansions of the number 29/343 terminating decimal expansions.
Answer» We know, 29/343 = 29/7³ Given rational number is 29/343 p/q is terminating if a) p and q are co-prime & b) q is of the form of 2ⁿ 5^m where n and m are non-negative integers. Firstly we check co-prime 29 = 29 × 1 343 = 7 × 7 × 7 29 and 343 have no common factors Therefore, 29 and 343 are co-prime. Now, we have to check that q is in the form of 2ⁿ5^m 343 = 7³ So, the denominator is not of the form 2ⁿ5^m Thus, 29/343 is a non-terminating repeating decimal.

Write down the decimal expansions of the number 29/343 terminating decimal expansions.

Answer»

We know, 29/343 = 29/7³

Given rational number is 29/343

p/q is terminating if

a) p and q are co-prime &

b) q is of the form of 2ⁿ 5^m where n and m are non-negative integers.

Firstly we check co-prime

29 = 29 × 1

343 = 7 × 7 × 7

29 and 343 have no common factors

Therefore, 29 and 343 are co-prime.

Now, we have to check that q is in the form of 2ⁿ5^m

343 = 7³

So, the denominator is not of the form 2ⁿ5^m

Thus, 29/343 is a non-terminating repeating decimal.