QuestionMultiply or divide these measurements, ensuring correct significant digits:
1. $2.094 \mathrm{~cm} \times 1.10 \mathrm{~cm} = \square \mathrm{cm}^{2}$
2. $20.94 \frac{\mathrm{g}}{\mathrm{mL}} \times 33 \mathrm{mL} = \square \mathrm{g}$
3. $496.3 \mathrm{~m} \div 0.90 \mathrm{~s} = \square \frac{\mathrm{m}}{\mathrm{s}}$

Studdy Solution

STEP 1

Assumptions1. The multiplication and division operations are to be performed as they are. . The number of significant digits in the result should be equal to the number of significant digits in the least precise measurement used in the calculations.

STEP 2

First, let's multiply the measurements in the first problem.
$Product =2.094\, cm \times1.10\, cm$

STEP 3

Perform the multiplication operation.
$Product =2.094 \times1.10 =2.303\, cm^2$

STEP 4

Now, we need to round the result to the correct number of significant digits. The least precise measurement is1.10 cm, which has3 significant digits. Therefore, the result should also have3 significant digits.
$Product =2.30\, cm^2$

STEP 5

Next, let's multiply the measurements in the second problem.
$Product =20.94\, \frac{g}{m} \times33\, mL$

STEP 6

Perform the multiplication operation.
$Product =20.94 \times33 =691.02\, g$

STEP 7

Now, we need to round the result to the correct number of significant digits. The least precise measurement is33 mL, which has2 significant digits. Therefore, the result should also have2 significant digits.
$Product =690\, g$

STEP 8

Finally, let's divide the measurements in the third problem.
$Quotient =496.3\, m \div0.90\, s$

STEP 9

Perform the division operation.
$Quotient =496.3 \div.90 =551.444... \frac{m}{s}$

STEP 10

Now, we need to round the result to the correct number of significant digits. The least precise measurement is0.90 s, which has2 significant digits. Therefore, the result should also have2 significant digits.
$Quotient =550\, \frac{m}{s}$ So, the solutions are $\begin{array}{c} 2.094 \mathrm{~cm} \times.10 \mathrm{~cm}=2.30 \mathrm{cm}^{2} \\ 20.94 \frac{\mathrm{g}}{\mathrm{m}} \times33 . \mathrm{~m}=690 \mathrm{~g} \\ 496.3 \mathrm{~m} \div0.90 \mathrm{~s}=550 \frac{\mathrm{m}}{\mathrm{s}} \end{array}$

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Studdy Solution

STEP 1

Assumptions1. The multiplication and division operations are to be performed as they are. . The number of significant digits in the result should be equal to the number of significant digits in the least precise measurement used in the calculations.

STEP 2

First, let's multiply the measurements in the first problem.
$Product =2.094\, cm \times1.10\, cm$

STEP 3

Perform the multiplication operation.
$Product =2.094 \times1.10 =2.303\, cm^2$

STEP 4

Now, we need to round the result to the correct number of significant digits. The least precise measurement is1.10 cm, which has3 significant digits. Therefore, the result should also have3 significant digits.
$Product =2.30\, cm^2$

STEP 5

Next, let's multiply the measurements in the second problem.
$Product =20.94\, \frac{g}{m} \times33\, mL$

STEP 6

Perform the multiplication operation.
$Product =20.94 \times33 =691.02\, g$

STEP 7

Now, we need to round the result to the correct number of significant digits. The least precise measurement is33 mL, which has2 significant digits. Therefore, the result should also have2 significant digits.
$Product =690\, g$

STEP 8

Finally, let's divide the measurements in the third problem.
$Quotient =496.3\, m \div0.90\, s$

STEP 9

Perform the division operation.
$Quotient =496.3 \div.90 =551.444... \frac{m}{s}$

STEP 10

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Studdy Solution

STEP 1

Assumptions1. The multiplication and division operations are to be performed as they are. . The number of significant digits in the result should be equal to the number of significant digits in the least precise measurement used in the calculations.

STEP 2

First, let's multiply the measurements in the first problem.Product=2.094 cm×1.10 cmProduct =2.094\, cm \times1.10\, cmProduct=2.094cm×1.10cm

STEP 3

Perform the multiplication operation.Product=2.094×1.10=2.303 cm2Product =2.094 \times1.10 =2.303\, cm^2Product=2.094×1.10=2.303cm2

STEP 4

Now, we need to round the result to the correct number of significant digits. The least precise measurement is1.10 cm, which has3 significant digits. Therefore, the result should also have3 significant digits.Product=2.30 cm2Product =2.30\, cm^2Product=2.30cm2

STEP 5

Next, let's multiply the measurements in the second problem.Product=20.94 gm×33 mLProduct =20.94\, \frac{g}{m} \times33\, mLProduct=20.94mg​×33mL

STEP 6

Perform the multiplication operation.Product=20.94×33=691.02 gProduct =20.94 \times33 =691.02\, gProduct=20.94×33=691.02g

STEP 7

Now, we need to round the result to the correct number of significant digits. The least precise measurement is33 mL, which has2 significant digits. Therefore, the result should also have2 significant digits.Product=690 gProduct =690\, gProduct=690g

STEP 8

Finally, let's divide the measurements in the third problem.Quotient=496.3 m÷0.90 sQuotient =496.3\, m \div0.90\, sQuotient=496.3m÷0.90s

STEP 9

Perform the division operation.Quotient=496.3÷.90=551.444...msQuotient =496.3 \div.90 =551.444... \frac{m}{s}Quotient=496.3÷.90=551.444...sm​

STEP 10

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First, let's multiply the measurements in the first problem.
$Product =2.094\, cm \times1.10\, cm$

Perform the multiplication operation.
$Product =2.094 \times1.10 =2.303\, cm^2$

Now, we need to round the result to the correct number of significant digits. The least precise measurement is1.10 cm, which has3 significant digits. Therefore, the result should also have3 significant digits.
$Product =2.30\, cm^2$

Next, let's multiply the measurements in the second problem.
$Product =20.94\, \frac{g}{m} \times33\, mL$

Perform the multiplication operation.
$Product =20.94 \times33 =691.02\, g$

Now, we need to round the result to the correct number of significant digits. The least precise measurement is33 mL, which has2 significant digits. Therefore, the result should also have2 significant digits.
$Product =690\, g$

Finally, let's divide the measurements in the third problem.
$Quotient =496.3\, m \div0.90\, s$

Perform the division operation.
$Quotient =496.3 \div.90 =551.444... \frac{m}{s}$