Question

A number \[5.78 \times {10^3}\] is wrongly written as \[5.87 \times {10^3}\]. Find the error.
A.1.56%
B.1.86%
C.1.76%
D.1.36%

Answer 1

Hint: The number is wrongly written so there must be some difference in the two numbers. Thus using formula for percentage change we will calculate the error.
Formula used:
\[\% error = \dfrac{{newvalue - oldvalue}}{{oldvalue}} \times 100\]

Complete step-by-step answer:
Given that \[5.78 \times {10^3}\]is the number to be written. It means this is the old value.
But it was written instead \[5.87 \times {10^3}\].so this is the new value.
Now using the formula,
\[\% error = \dfrac{{newvalue - oldvalue}}{{oldvalue}} \times 100\]
\[
   \Rightarrow \dfrac{{5.87 \times {{10}^3} - 5.78 \times {{10}^3}}}{{5.78 \times {{10}^3}}} \times 100 \\
   \Rightarrow \dfrac{{0.09 \times {{10}^3}}}{{5.78 \times {{10}^3}}} \times 100 \\
\]
\[{10^3}\] Cancels from numerator and denominator.
\[
   \Rightarrow 1.557\% \\
   \Rightarrow \approx 1.56\% \\
\]
Thus rounded off value is 1.56%.
Thus option A is correct.

Note: When we find the error percentage always compare it with the originally written value as in this problem or in general with old value.
This formula is also used in finding percentage change in areas, increase or decrease in percentage or population of a town or city , increment or decrement in salary etc.