QuestionDivide and multiply these measurements, ensuring correct significant digits:
173.39 mol ÷ 0.61 L = \square mol/L 7.8084 mol/L × 2.3 L = \square mol 714.4 m ÷ 39.05 s = \square m/s

Studdy Solution

STEP 1

Assumptions1. The given measurements are in the correct units. . The rules for significant digits are followed - All non-zero digits are considered significant. - Any zeros between significant digits are significant. - Leading zeros are not significant. - Trailing zeros are significant only if they are after a decimal point.
3. When multiplying or dividing, the result should have the same number of significant figures as the measurement with the least number of significant figures.

STEP 2

First, let's solve the first problem. We need to divide173.39 mol by0.61 L.
$\frac{173.39 \, \mathrm{mol}}{0.61 \, \mathrm{}}$

STEP 3

Perform the division.
$\frac{173.39 \, \mathrm{mol}}{0.61 \, \mathrm{}} =284.0983606557377 \, \frac{\mathrm{mol}}{\mathrm{}}$

STEP 4

Now, we need to round this to the correct number of significant figures. The number with the least significant figures in the problem is0.61 L, which has two significant figures. Therefore, our answer should also have two significant figures.
$284.0983606557377 \, \frac{\mathrm{mol}}{\mathrm{}} \approx280 \, \frac{\mathrm{mol}}{\mathrm{}}$

STEP 5

Next, let's solve the second problem. We need to multiply7.8084 mol/L by2.3 L.
$7.8084 \, \frac{\mathrm{mol}}{\mathrm{}} \times2.3 \, \mathrm{}$

STEP 6

Perform the multiplication.
$.8084 \, \frac{\mathrm{mol}}{\mathrm{}} \times2.3 \, \mathrm{} =17.95932 \, \mathrm{mol}$

STEP 7

Now, we need to round this to the correct number of significant figures. The number with the least significant figures in the problem is2.3 L, which has two significant figures. Therefore, our answer should also have two significant figures.
$17.95932 \, \mathrm{mol} \approx18 \, \mathrm{mol}$

STEP 8

Finally, let's solve the third problem. We need to divide714.4 m by39.05 s.
$\frac{714.4 \, \mathrm{m}}{39.05 \, \mathrm{s}}$

STEP 9

Perform the division.
$\frac{714.4 \, \mathrm{m}}{39.05 \, \mathrm{s}} =18.29347181008902 \, \frac{\mathrm{m}}{\mathrm{s}}$

STEP 10

Now, we need to round this to the correct number of significant figures. The number with the least significant figures in the problem is39.05 s, which has four significant figures. Therefore, our answer should also have four significant figures.
$18.29347181008902 \, \frac{\mathrm{m}}{\mathrm{s}} \approx18.29 \, \frac{\mathrm{m}}{\mathrm{s}}$ So, the solutions to the problems are. $173.39 \, \mathrm{mol} \div0.61 \, \mathrm{} =280 \, \frac{\mathrm{mol}}{\mathrm{}}$ 2. $7.8084 \, \frac{\mathrm{mol}}{\mathrm{}} \times2.3 \, \mathrm{} =18 \, \mathrm{mol}$ 3. $714.4 \, \mathrm{m} \div39.05 \, \mathrm{s} =18.29 \, \frac{\mathrm{m}}{\mathrm{s}}$

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