A number 5.78 x 10³ is wrongly written as 5.87 x 10³; find the percentage error.

Given:

Incorrect number = 5.87 x 10³ = 5,870

Correct number = 5.78 x 10³ = 5,780

Difference = Correct number - Incorrect number

Difference = 5,780 - 5,870

Difference = -90

(Negative sign shows that value is decreasing.)

Percentage error = $\dfrac{\text{difference}}{\text{correct number}} \times 100$ %

= $\dfrac{90}{5,780} \times 100$ %

= $\dfrac{9,000}{5,780}$ %

= $\dfrac{900}{578}$ %

= 1.56 %

The percentage error = 1.56%.