A lab technician weighs crystals of a blue salt. Each has mass \(2.4 \times 10^{-5}\) grams. She counts out 5000 crystals for a test. Work out the total mas...
Question 1 Report
A lab technician weighs crystals of a blue salt. Each has mass \(2.4 \times 10^{-5}\) grams. She counts out 5000 crystals for a test.
Work out the total mass of these crystals. Give your answer in standard form. (2)
Answer Details
Standard form writes a number as \(a \times 10^n\) where \(1 \leq a < 10\) and \(n\) is an integer. The plan is to multiply the number parts and the powers of ten separately, then adjust so that the number part lies in range.
Writing \(5000\) as \(5 \times 10^3\) first makes the powers easy to combine:
\[2.4 \times 10^{-5} \times 5 \times 10^{3} = (2.4 \times 5) \times (10^{-5} \times 10^{3}) = 12 \times 10^{-2}\]The indices are added, since \(-5 + 3 = -2\). [1]
This is not yet standard form, because \(12\) is not between \(1\) and \(10\). Rewriting \(12\) as \(1.2 \times 10^{1}\) and combining the powers again:
\[12 \times 10^{-2} = 1.2 \times 10^{1} \times 10^{-2} = 1.2 \times 10^{-1} \text{ grams}\][1]
The total mass is \(1.2 \times 10^{-1}\) g, that is \(0.12\) g.
The final tidying step is where marks are usually lost. When the number part is made ten times smaller, the index must go up by one to compensate, so \(12 \times 10^{-2}\) becomes \(1.2 \times 10^{-1}\) and not \(1.2 \times 10^{-3}\).
Download The App On Google Playstore
Everything you need to excel in your exams
