Carry out the following operations and express the answers...

Carry out the following operations and express the answers with the appropriate number of significant figures. $$ \begin{array}{ll}{\text { (a) } 14.3505+2.65} & {\text { (b) } 952.7-140.7389} \\ {\text { (c) }\left(3.29 \times 10^{4}\right)(0.2501)} & {\text { (d) } 0.0588 / 0.677}\end{array} $$

Carry out the following operations and express the answers with the appropriate number of significant figures.
$$
\begin{array}{ll}{\text { (a) } 14.3505+2.65} & {\text { (b) } 952.7-140.7389} \\ {\text { (c) }\left(3.29 \times 10^{4}\right)(0.2501)} & {\text { (d) } 0.0588 / 0.677}\end{array}
$$

Key Concepts

Significant Figures

Significant figures are the digits in a number that contribute to its precision. They represent the measured or known quantities and are used to indicate the confidence or uncertainty in a value. The rules of significant figures help determine how precise the result of a calculation should be, ensuring that the precision of the measured data is maintained in the final answer.

Addition and Subtraction Rules

When adding or subtracting quantities, the result should be reported with the same number of decimal places as the measurement with the fewest decimal places. This rule reflects the fact that the uncertainty is carried in the decimal part of the number during addition or subtraction, and it ensures that the precision of the result does not exceed that of the least precise measurement.

Multiplication and Division Rules

For multiplication and division, the number of significant figures in the final result should be the same as the measurement with the fewest significant figures among those being multiplied or divided. This method maintains the relative precision of the measurements and reflects the inherent uncertainty in the values being combined.

Rounding

Rounding is the process of adjusting the digits of a number so that it contains the correct number of significant figures according to the rules of the operations. This ensures that the final answer accurately reflects the limitations and precision of the original measurements, and prevents the appearance of false precision in the result.

Transcript

00:01 So when we're adding and subtracting significant figures, we answer the question to the least accurate value.

00:10 So for instance, if we had two decimal places for one number and four decimal places for the other, we're only going to answer it to two decimal places.

00:20 In multiplication and division, we answer to the least number of significant figures.

00:25 So if we had something with five significant figures and something with four significant figures, here's we'd only answer to four.

00:33 Let's look at some examples.

00:35 And let's start with addition.

00:38 So if we take the numbers 14 .3505 and add 2 .65 to that, what we're going to do is we're going to take our total answer here, which is going to be our 17.

01:01 17 .005.

01:06 But if we look, the hundreds place is our least accurate value.

01:13 So what we're gonna do is we're gonna chop the answer off here.

01:17 And so the answer is gonna be 17 .00.

01:23 Remember that numbers are measured when we're using significant figures.

01:28 They're not exact numbers.

01:30 And so we only go to the least accurate amount of precision that we have.

01:38 If we take a look at some subtraction, if we have 952 .7 minus 140 .7389.

01:54 We're going to wind up doing the same thing.

01:59 And if we were to take a look at this, we would get an answer of 811 .11.

02:10 But 9611, but we can only answer to the 10th place, the least accurate decimal...