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Question 45

For an experimental expression $$y=\frac{32.3\times1125}{27.4},$$ where all the digits are significant. Then to report the value of  $$y$$  we should write

We need to compute $$y = \frac{32.3 \times 1125}{27.4}$$ and report it with the correct number of significant figures.

First, let us count the significant figures in each quantity:
$$32.3$$ has 3 significant figures.
$$1125$$ has 4 significant figures.
$$27.4$$ has 3 significant figures.

In multiplication and division, the final result must have the same number of significant figures as the quantity with the fewest significant figures. Here, the minimum is 3 significant figures.

Now let us compute the value step by step.

$$32.3 \times 1125 = 36337.5$$

$$y = \frac{36337.5}{27.4} = 1326.186...$$

We must round this to 3 significant figures. The first three significant digits of $$1326.186$$ are $$1$$, $$3$$, and $$2$$. The next digit is $$6$$, which is $$\ge 5$$, so we round up.

$$1326.186... \approx 1330$$

Hence, the correct answer is Option B.

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