Question

2. Without performing division, state whether the following rational numbers will
have a terminating decimal form or a non-terminating repeating decimal form 29/343​

Answer 1

Answer:

non terminating

Step-by-step explanation:

343=7×7×7

all terminating decimal expansions have 2 or 5 as its prime factor of the denominator

since 343 don't have 2 or 5 as its prime factor so it will have non terminating decimal expansion

Answer 2

Step-by-step explanation:

We know that, a number is said to be rational if it can be represented in the p/q form, where p and q are integers, and q not equal to 0

so,

29/343 is a rational number where p = 29 and q = 343

For a number to terminate it must be divided by 10 or multiples of 10 (Think about it)

10 = 2 × 5

Now, a rational number is terminating if q is of the form

2^m × 5^n where m and n are intergers

Here, q = 343

now, 343 = 7 × 7 × 7

and they are not of the form 2^m × 5^n so, they will be non terminating rational number

Hope it helped and you understood it........All the best