Question 59: Units , Dimensions and Error Analysis

Question

For an experimental expression $y=\frac{32.3 	imes 1125}{27.4}$, where all the digits are significant. Then to report the value of $y$ we should write

Accepted Answer

$$ 32.3 \quad (3\ 	ext{sig figs}), \quad 1125 \quad (4\ 	ext{sig figs}), \quad 27.4 \quad (3\ 	ext{sig figs}) $$
In multiplication and division, the final answer must be reported with the same number of significant figures as the factor with the fewest significant figures, which here is 3.
First, calculate the unrounded result:
$$ y = \frac{32.3 	imes 1125}{27.4} \approx \frac{36337.5}{27.4} \approx 1326.186 $$
Expressing $1326.186$ in scientific notation:
$$ 1326.186 \approx 1.326186 	imes 10^3 $$
Rounding to 3 significant figures:
The first three significant digits are 1, 3, and 2.
Considering the fourth digit (6) causes the last significant digit to round up.
Thus,
$$ 1.326186 	imes 10^3 \approx 1.33 	imes 10^3 $$
In standard decimal form, this is written as:
$$ 1330 $$
Hence, the final reported value is:
$$ y = 1330 $$

Answer

$y=1326.186$

Answer

$y=1326.2$

Answer

$y=1326.19$

Answer

$y=1330$

Units , Dimensions and Error Analysis

For an experimental expression y=\frac{32.3 \times 1125}{27.4}, where all the digits are significant. Then to report the value of y we should write

Choose the correct answer: