Math

QuestionMultiply or divide these measurements with proper significant digits:
1. 20.947gmL×32mL=g20.947 \frac{\mathrm{g}}{\mathrm{mL}} \times 32 \mathrm{mL} = \square \mathrm{g}
2. 914.4g÷0.65mL=gmL914.4 \mathrm{g} \div 0.65 \mathrm{mL} = \square \frac{\mathrm{g}}{\mathrm{mL}}
3. 0.934cm×1.125cm=cm20.934 \mathrm{cm} \times 1.125 \mathrm{cm} = \square \mathrm{cm}^{2}

Studdy Solution

STEP 1

Assumptions1. The given measurements are in the correct units. . The multiplication or division should be carried out as indicated.
3. The number of significant digits in the final answer should match the number of significant digits in the measurement with the least number of significant digits.

STEP 2

For the first measurement, we need to multiply the given values.20.947gm×32.m20.947 \frac{\mathrm{g}}{\mathrm{m}} \times32 . \mathrm{m}

STEP 3

Carry out the multiplication.
20.947gm×32.m=670.304g20.947 \frac{\mathrm{g}}{\mathrm{m}} \times32 . \mathrm{m} =670.304 \mathrm{g}

STEP 4

The final answer should have the same number of significant digits as the measurement with the least number of significant digits. In this case, it's32 mL, which has2 significant digits. So, we round the final answer to2 significant digits.
670.304g670g670.304 \mathrm{g} \approx670 \mathrm{g}

STEP 5

For the second measurement, we need to divide the given values.
914.4 g÷0.65 m914.4 \mathrm{~g} \div0.65 \mathrm{~m}

STEP 6

Carry out the division.
914.4 g÷0.65 m=1406.7692307692307692307692307692gm914.4 \mathrm{~g} \div0.65 \mathrm{~m} =1406.7692307692307692307692307692 \frac{\mathrm{g}}{\mathrm{m}}

STEP 7

The final answer should have the same number of significant digits as the measurement with the least number of significant digits. In this case, it's0.65 mL, which has2 significant digits. So, we round the final answer to2 significant digits.
1406.7692307692307692307692307692gm1400gm1406.7692307692307692307692307692 \frac{\mathrm{g}}{\mathrm{m}} \approx1400 \frac{\mathrm{g}}{\mathrm{m}}

STEP 8

For the third measurement, we need to multiply the given values.
0.934 cm×1.125 cm0.934 \mathrm{~cm} \times1.125 \mathrm{~cm}

STEP 9

Carry out the multiplication.
.934 cm×.125 cm=.05025cm2.934 \mathrm{~cm} \times.125 \mathrm{~cm} =.05025 \mathrm{cm}^{2}

STEP 10

The final answer should have the same number of significant digits as the measurement with the least number of significant digits. In this case, it's0.934 cm, which has3 significant digits. So, we round the final answer to3 significant digits.
.05025cm2.05cm2.05025 \mathrm{cm}^{2} \approx.05 \mathrm{cm}^{2}The final answers are-670 g-1400 g/mL-.05 cm²

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