Question

1. (4 pts) a chemist wants to add these 2 measurements together: 2.30040 × 10^6 ml and 7,345.6 ml. what can she report as the correct combined volume? (a) 2,307,745.6 ml (b) 2,307,750 ml (c) 2,307,700 ml (d) none of the above

Explanation:

Step1: Add the two volumes

$$2.30040\times10^{6}+7345.6$$
$$=2300400 + 7345.6$$
$$=2307745.6$$

Step2: Consider significant figures

The first number \(2.30040\times10^{6}\) has six significant figures, and the second number \(7345.6\) has five significant figures. When adding, we go by the least number of decimal places. But in terms of significant - figure rules for addition (which is more about the least precise measurement in terms of decimal places, but when one is in scientific notation and the other is a whole number with a decimal, we can also think about the overall magnitude). The first number \(2.30040\times10^{6}=2300400\) (the last non - zero digit before the power of 10 is in the units place when expanded). The second number \(7345.6\) has the last significant digit in the tenths place. However, when we add them \(2300400+7345.6 = 2307745.6\). But if we consider the rules for significant figures in addition (the result should be rounded to the same decimal place as the least precise measurement). The first number \(2.30040\times10^{6}\) (if we consider its precision in terms of the digit after the decimal in scientific notation, it's precise to the ten - thousands place: \(2.30040\times10^{6}=2300400\), the \(4\) is in the ten - thousands place). The second number \(7345.6\) is precise to the tenths place. But another way is to note that when we add \(a\times10^{n}\) and \(b\) (\(n\) is large), the result's significant figures are mainly determined by \(a\times10^{n}\). But actually, when we add \(2300400+7345.6 = 2307745.6\), and if we consider the rules for significant figures in addition (the number of decimal places), the first number \(2.30040\times10^{6}\) (if written as \(2300400.0\)) has one decimal place (in the expanded form with a decimal added for clarity of decimal - place counting), and \(7345.6\) has one decimal place. So \(2307745.6\) is the sum.

Answer:

A. \(2,307,745.6\space mL\)