A community library's humidity sensor logs two readings in the same units, given in standard form as \(2.3 \times 10^{-3}\) and \(4.7 \times 10^{-4}\). Use ...
Question 1 Report
A community library's humidity sensor logs two readings in the same units, given in standard form as \(2.3 \times 10^{-3}\) and \(4.7 \times 10^{-4}\). Use your calculator to work out their sum, giving your answer in standard form. (2)
Answer Details
To add numbers given in standard form with different powers of \(10\), it is simplest to convert both to ordinary decimals first, add them, then convert the result back to standard form. Here \(2.3 \times 10^{-3} = 0.0023\) and \(4.7 \times 10^{-4} = 0.00047\), so their sum is \(0.0023+0.00047 = 0.00277\). [1 mark]
Writing \(0.00277\) in standard form, \(a \times 10^{n}\) with \(1 \leqslant a < 10\), gives \(2.77 \times 10^{-3}\). [1 mark]
Adding directly in standard form only works cleanly when the powers of \(10\) already match; since they differ here, converting to decimals first avoids a common error of adding the two numbers \(2.3\) and \(4.7\) without accounting for their different place values.
Download The App On Google Playstore
Everything you need to excel in your exams
