Question

Without using a calculator or computing by hand, determine if the fraction 413/1400 has a terminating or repeating decimal. Explain your reasoning.

Answer #1

PROPERTY --- The fraction (p/q) { where p and q are co-primes } has a TERMINATING DECIMAL if the denominator q is of the form ( 2^m * 5^n ) where m and n are natural numbers.

Given fraction is 413/1400

In standard form , 413/1400 = 59/200

Now , the denominator is 200

200 = 2^3 * 5^2

Clearly , 200 is of the from 2^m * 5^n where m = 3 and n = 2

Thus

The given fraction has TERMINATING DECIMAL.

As we know ,

413/1400 = 59/200 = 0.295

Hope you understand the solution.

Thanks.

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