Question

carry out the following calculation and report the answer using the proper number of significant figures: 46.39 + 1.756 options: 48, 48.1, 48.14, 48.15, 48.146

Explanation:

Step1: Add the two numbers

First, we calculate the sum of \( 46.39 \) and \( 1.756 \).
\( 46.39 + 1.756 = 48.146 \)

Step2: Determine significant figures

Now, we need to consider the number of significant figures. When adding, the result should have the same number of decimal places as the number with the least decimal places. \( 46.39 \) has two decimal places, and \( 1.756 \) has three. So we round to two decimal places? Wait, no, actually, for significant figures in addition, we look at the precision (decimal places). But let's check the original numbers: \( 46.39 \) has four significant figures, \( 1.756 \) has four. When adding, the result's precision is determined by the least precise measurement. \( 46.39 \) is precise to the hundredth place, \( 1.756 \) to the thousandth. So the sum should be precise to the hundredth place? Wait, no, let's do the addition:

\( 46.39 + 1.756 = 48.146 \)

Now, let's check the options. The options are 48, 48.1, 48.14, 48.15, 48.146.

Wait, maybe we need to consider significant figures based on the original numbers. \( 46.39 \) has four significant figures, \( 1.756 \) has four. The sum is \( 48.146 \). Now, let's see the decimal places: \( 46.39 \) has two decimal places, \( 1.756 \) has three. So when adding, the result should be rounded to two decimal places? Wait, \( 48.146 \) rounded to two decimal places is \( 48.15 \)? Wait, no: the third decimal is 6, which is more than 5, so we round up the second decimal: 4 becomes 5. So \( 48.15 \)? Wait, but let's check the addition again.

Wait, \( 46.39 + 1.756 \):

\( 46.39 \)
\( +1.756 \)
\( ------- \)
\( 48.146 \)

Now, \( 46.39 \) has two decimal places, so the sum should be reported to two decimal places. So \( 48.146 \) rounded to two decimal places: look at the third decimal, which is 6. So we round up the second decimal: 4 + 1 = 5. So \( 48.15 \). Wait, but let's check the options. One of the options is 48.15. Alternatively, maybe we consider significant figures in terms of the number of significant figures. Wait, \( 46.39 \) has four, \( 1.756 \) has four. The sum is \( 48.146 \), which has five significant figures? No, wait, \( 48.146 \) has five significant figures. But maybe the question is about decimal places or significant figures. Wait, the options include 48.146 (the exact sum), 48.15, 48.14, etc.

Wait, maybe I made a mistake. Let's recalculate:

\( 46.39 + 1.756 = 48.146 \)

Now, let's check the decimal places: \( 46.39 \) is to the hundredth (two decimal places), \( 1.756 \) to the thousandth (three). So the sum should be to the hundredth place (two decimal places) because \( 46.39 \) is less precise. So we round \( 48.146 \) to two decimal places: the third decimal is 6, so we round up the second decimal: 4 becomes 5. So \( 48.15 \). So the correct option is 48.15.

Answer:

48.15 (corresponding to the option "48.15")