The number line shows four masses, in kilograms: \(3\times10^{-2}\), \(7\times10^{-3}\), \(5\times10^{-2}\) and \(2\times10^{-1}\). Work out the difference ...
Question 1 Report
The number line shows four masses, in kilograms: \(3\times10^{-2}\), \(7\times10^{-3}\), \(5\times10^{-2}\) and \(2\times10^{-1}\).
Work out the difference between the largest mass and the smallest mass, giving your answer in standard form.
Answer Details
First identify which of the four masses is largest and which is smallest by comparing the powers of ten, since the index governs size. Writing each as an ordinary number makes the comparison clear.
| Standard form | Mass in kg |
|---|---|
| \( 7 \times 10^{-3} \) | \( 0.007 \) |
| \( 3 \times 10^{-2} \) | \( 0.03 \) |
| \( 5 \times 10^{-2} \) | \( 0.05 \) |
| \( 2 \times 10^{-1} \) | \( 0.2 \) |
The largest is \( 2 \times 10^{-1} \) and the smallest is \( 7 \times 10^{-3} \), since \( -1 \) is the least negative index and \( -3 \) the most negative [M1].
Now subtract. Numbers with different indices cannot have their front numbers subtracted directly, so use ordinary numbers [M1]:
\[ 0.2 - 0.007 = 0.193 \]In standard form the difference is \( 1.93 \times 10^{-1} \) kg [A1].
The trap is choosing \( 7 \times 10^{-3} \) as the largest because 7 is the biggest front number. With negative indices, a larger front number does not mean a larger value; the power of ten decides first.
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