Solve |41/512-231/256|

$$| \frac { 41 } { 512 } - \frac { 231 } { 256 } |$$

Evaluate

$$\frac{421}{512}=0.822265625$$

Solution Steps

Least common multiple of 512 and 256 is 512. Convert \frac{41}{512} and \frac{231}{256} to fractions with denominator 512.

$$|\frac{41}{512}-\frac{462}{512}|$$

Since \frac{41}{512} and \frac{462}{512} have the same denominator, subtract them by subtracting their numerators.

$$|\frac{41-462}{512}|$$

Subtract 462 from 41 to get -421.

$$|-\frac{421}{512}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{421}{512} is \frac{421}{512}.

$$\frac{421}{512}$$

Factor

$$\frac{421}{2 ^ {9}} = 0.822265625$$