Question

Without actually performing the long division state whether 13/3125and13/343will have a terminating decimal expansion or a non terminating repeating decimal expansion

Answer 1

1. 13/1325

1325=5× 5× 53= 5^2 × 53^ 1

This cannot be expressed as 2^m× 5^n

So the decimal expansion will be non terminating.

2. 13/343

343= 7×7×7

This cannot be expressed as 2^m× 5^n

So the decimal expansion will be non terminating.