The significant figure rules for addition and subtraction basically has you add or subtract as normal, but the rounding is where the rule kicks in. Specifically you round based on the least accurate decimal portion (the term with the least number of digits to the right of the decimal point).
We do this because we want to make sure we don't involve digits we aren't 100% sure of their accuracy.
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Part A
Add up the values like normal
32.567+135.0+1.4567 = 169.0237
Now we look at the decimal portions of each number. We look at the number of digits to the right of each decimal point.
32.567 has three such digits (5,6 and 7)
135.0 only has one digit (the 0)
1.4567 has four digits (4,5,6,7)
The least accurate is 135.0 since we only know this to the tenths place. So we'll be rounding the sum we got above (169.0237) to the nearest tenth
169.0237 rounds to 169.0
<h3>Answer before rounding = 169.0237</h3><h3>Answer after rounding = 169.0</h3>
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Part B
Add like normal
246.24+238.278+98.3 = 582.818
Then round to one decimal place since this is the fewest number of digits after the decimal point (in the number 98.3)
582.818 rounds to 582.8
<h3>Answer before rounding = 582.818</h3><h3>Answer after rounding = 582.8</h3>
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Part C
Subtraction is handled in a similar fashion
4.829-0.26 = 4.569
Which rounds to 4.57 since two digits is the smallest number of digits after the decimal point. Put another way, 0.26 is the least of the accurate measurements comparing 4.829 and 0.26; we always go with the least accurate or weakest link when it comes to rounding sig figs. If we went the other way around, then we could be introducing data that isn't really there.
<h3>Answer before rounding = 4.569</h3><h3>Answer after rounding = 4.57</h3>
