A student was asked to approximate the fraction \frac{5}{16} as a decimal rounded to 2 sig… — JAMB UTME

A student was asked to approximate the fraction $\frac{5}{16}$ as a decimal rounded to $2$ significant figures. What is the percentage error introduced by this approximation?

$0.8\%Answer
B
$0.81\%
C
$0.16\%
D
$0.008\%

Answer

The percentage error introduced by the approximation is

0.8\%

Converting

\frac{5}{16}

gives

0.3125

. Rounding to

2

significant figures gives an estimated value of

0.31

. The absolute error is

|0.31 - 0.3125| = 0.0025

. Dividing by the true value

0.3125

yields a relative error of

0.008

, which equals

0.8\%

when multiplied by

100\%

Step-by-Step Solution

Convert the fraction to an exact decimal

\frac{5}{16} = 0.3125

To find the true value of the number before approximation.

Round the exact decimal to 2 significant figures

0.3125 \approx 0.31

The first non-zero digits are 3 and 1; the next digit (2) is less than 5, so we round down.

Calculate the absolute error

|0.31 - 0.3125| = 0.0025

Absolute error is the magnitude of the difference between actual and estimated values.

Calculate the percentage error

\frac{0.0025}{0.3125} \times 100\% = 0.8\%

Percentage error is given by

\frac{\text{Absolute Error}}{\text{True Value}} \times 100\%

Key Concept

Fractions, Decimals, Percentages, and Approximations

Estimated Time:1m 15s

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