Question

1. express the answer to each of the following calculations with the correct number of significant figures,

\ta) 3.42 + 8.132 \t\t\t\td) 3.882 - 2.1
\tb) 4.9 + 3.822 \t\t\t\te) 4.894 - 2.03
\tc) 17.8 + 12.115 \t\t\tf) 15.6600 - 12.838

Explanation:

Part a)

Step1: Add the numbers

$3.42 + 8.132 = 11.552$

Step2: Determine significant figures (decimal places)

3.42 has 2 decimal places, 8.132 has 3. We round to 2 decimal places.
$11.552 \approx 11.55$ (Wait, no: when adding, the result should have the same number of decimal places as the least precise measurement. 3.42 has 2 decimal places, so we round to 2 decimal places. But 11.552 rounded to 2 decimal places is 11.55? Wait, no, 3.42 + 8.132 = 11.552. The least number of decimal places is 2 (from 3.42). So we look at the third decimal place (2) which is less than 5, so we keep the second decimal place as is? Wait, no, 11.552: the first number has two decimal places, so the sum should have two decimal places. So 11.55? Wait, no, 3.42 is to the hundredth place, 8.132 to the thousandth. So the sum should be to the hundredth place. 11.552 rounded to the hundredth place: the thousandth digit is 2, which is less than 5, so we round down. So 11.55? Wait, no, 3.42 + 8.132 = 11.552. So the correct rounding is to two decimal places: 11.55? Wait, no, 3.42 has two decimal places, so the result should have two decimal places. So 11.55? Wait, actually, 3.42 + 8.132 = 11.552. The rule for addition/subtraction is that the result has the same number of decimal places as the term with the least number of decimal places. 3.42 has 2 decimal places, 8.132 has 3. So we round to 2 decimal places. 11.552 rounded to 2 decimal places: look at the third decimal place (2), which is less than 5, so we keep the second decimal place as 5. So 11.55? Wait, no, 11.552: the first decimal place is 5, second is 5, third is 2. So rounding to two decimal places: 11.55.

Step1: Add the numbers

$4.9 + 3.822 = 8.722$

Step2: Determine decimal places

4.9 has 1 decimal place, 3.822 has 3. Round to 1 decimal place.
$8.722 \approx 8.7$ (since the second decimal place is 2, less than 5, round down)

Step1: Add the numbers

$17.8 + 12.115 = 29.915$

Step2: Determine decimal places

17.8 has 1 decimal place, 12.115 has 3. Round to 1 decimal place.
$29.915 \approx 29.9$ (the second decimal place is 1, less than 5, round down)

Answer:

$11.55$ (Wait, no, wait: 3.42 + 8.132 = 11.552. The number with the least decimal places is 3.42 (2 decimal places). So we round to 2 decimal places. 11.552: the third decimal is 2, so we round down. So 11.55. But wait, maybe I made a mistake. Let's check again. 3.42 is 3.420 (if we consider decimal places), 8.132 is 8.132. Adding them: 3.420 + 8.132 = 11.552. Now, the least number of decimal places is 2 (from 3.42, which is 3.420 with three decimal places? Wait, no: 3.42 has two decimal places (the 2 is in the hundredth place), 8.132 has three (thousandth). So when adding, we go by the number of decimal places, not the number of significant figures. So the result should have two decimal places. So 11.552 rounded to two decimal places: the third decimal is 2, so we round down. So 11.55.

Part b)