Use your calculator to work out \(\frac{\sqrt{20.4}-1.9}{0.32\times 4.7}\). Give your answer correct to 3 significant figures.

The fraction bar acts as a bracket around both the numerator and the denominator, so each must be fully evaluated before the division. Entering the expression as written from left to right, without brackets, would divide only \(1.9\) by \(0.32\) and then multiply by \(4.7\), giving a completely different value.

1. Numerator. \(\sqrt{20.4}=4.51663\ldots\), so \(4.51663\ldots-1.9=2.61663\ldots\)
2. Denominator. \(0.32\times 4.7=1.504\)
3. Divide. \[\frac{2.61663\ldots}{1.504}=1.7397\ldots\] [M1]

The answer correct to 3 significant figures is \(1.74\). [A1] cao

On the calculator, enter it in one go using the fraction template, or type it as \((\sqrt{20.4}-1.9)\div(0.32\times 4.7)\) with both sets of brackets. Rounding \(\sqrt{20.4}\) to \(4.52\) before subtracting shifts the answer to \(1.741\), which still rounds correctly here but will not always do so. Carry full accuracy to the last step.