Question

How do you evaluate the following expression using decimals?: `4.136 - 8.2612 + 77/64 + 205/128`

Answer 1

`4.136-8.2612+77/64+205/128=-1.3205125`

Explanation:

Here `77/64` and `205/128` have only `2` as prime factors for denominators. In fact they are `2^6` and `2^7` and hence they can be converted into decimal form by multiplying numerator and denominator by `5^6=15625` and `5^7=78125`.

Hence `77/64=1.203125` and `205/128=1.6015625`.

Hence `4.136-8.2612+1.203125+1.6015625=-1.3205125`