Solved on Jan 25, 2024

Divide $\frac{2.38 \times 10^{-2}}{8.5 \times 10^{4}}$ and select the correct answer from the options: $2.8 \times 10^{-7}$ , $2.7 \times 10^{-7}$ , $3.9 \times 10^{-7}$ , $5.7 \times 10^{-7}$ .

STEP 1

Assumptions
1. We are given the division problem $\frac{2.38 \times 10^{-2}}{8.5 \times 10^{4}}$ .
2. We need to simplify the expression to find the quotient.
3. The quotient should be expressed in scientific notation.

STEP 2

To divide two numbers in scientific notation, we divide their coefficients (the numbers in front of the powers of 10) and subtract the exponent of the denominator from the exponent of the numerator.
$\frac{a \times 10^{m}}{b \times 10^{n}} = \frac{a}{b} \times 10^{m-n}$

STEP 3

Apply the rule from STEP_2 to the given problem.
$\frac{2.38 \times 10^{-2}}{8.5 \times 10^{4}} = \frac{2.38}{8.5} \times 10^{-2 - 4}$

STEP 4

Subtract the exponents of 10.
$10^{-2 - 4} = 10^{-6}$

STEP 5

Now we divide the coefficients.
$\frac{2.38}{8.5}$

STEP 6

Perform the division.
$\frac{2.38}{8.5} \approx 0.28$

STEP 7

Combine the result of the division of coefficients with the result of the subtraction of exponents.
$0.28 \times 10^{-6}$

STEP 8

The result in STEP_7 is not in proper scientific notation because the coefficient should be a number between 1 and 10. To convert it to proper scientific notation, we need to adjust the coefficient and the exponent.
$0.28 \times 10^{-6} = 2.8 \times 10^{-7}$

STEP 9

Now we have the answer in proper scientific notation.
The correct answer is $2.8 \times 10^{-7}$ .

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Divide $\frac{2.38 \times 10^{-2}}{8.5 \times 10^{4}}$ and select the correct answer from the options: $2.8 \times 10^{-7}$ , $2.7 \times 10^{-7}$ , $3.9 \times 10^{-7}$ , $5.7 \times 10^{-7}$ .

STEP 1

Assumptions
1. We are given the division problem $\frac{2.38 \times 10^{-2}}{8.5 \times 10^{4}}$ .
2. We need to simplify the expression to find the quotient.
3. The quotient should be expressed in scientific notation.

STEP 2

To divide two numbers in scientific notation, we divide their coefficients (the numbers in front of the powers of 10) and subtract the exponent of the denominator from the exponent of the numerator.
$\frac{a \times 10^{m}}{b \times 10^{n}} = \frac{a}{b} \times 10^{m-n}$

STEP 3

Apply the rule from STEP_2 to the given problem.
$\frac{2.38 \times 10^{-2}}{8.5 \times 10^{4}} = \frac{2.38}{8.5} \times 10^{-2 - 4}$

STEP 4

Subtract the exponents of 10.
$10^{-2 - 4} = 10^{-6}$

STEP 5

Now we divide the coefficients.
$\frac{2.38}{8.5}$

STEP 6

Perform the division.
$\frac{2.38}{8.5} \approx 0.28$

STEP 7

Combine the result of the division of coefficients with the result of the subtraction of exponents.
$0.28 \times 10^{-6}$

STEP 8

The result in STEP_7 is not in proper scientific notation because the coefficient should be a number between 1 and 10. To convert it to proper scientific notation, we need to adjust the coefficient and the exponent.
$0.28 \times 10^{-6} = 2.8 \times 10^{-7}$

STEP 9

Now we have the answer in proper scientific notation.
The correct answer is $2.8 \times 10^{-7}$ .

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STEP 1

Assumptions1. We are given the division problem 2.38×10−28.5×104\frac{2.38 \times 10^{-2}}{8.5 \times 10^{4}}8.5×1042.38×10−2​.2. We need to simplify the expression to find the quotient.3. The quotient should be expressed in scientific notation.

STEP 2

STEP 3

Apply the rule from STEP_2 to the given problem.2.38×10−28.5×104=2.388.5×10−2−4\frac{2.38 \times 10^{-2}}{8.5 \times 10^{4}} = \frac{2.38}{8.5} \times 10^{-2 - 4}8.5×1042.38×10−2​=8.52.38​×10−2−4

STEP 4

Subtract the exponents of 10.10−2−4=10−610^{-2 - 4} = 10^{-6}10−2−4=10−6

STEP 5

Now we divide the coefficients.2.388.5\frac{2.38}{8.5}8.52.38​

STEP 6

Perform the division.2.388.5≈0.28\frac{2.38}{8.5} \approx 0.288.52.38​≈0.28

STEP 7

Combine the result of the division of coefficients with the result of the subtraction of exponents.0.28×10−60.28 \times 10^{-6}0.28×10−6

STEP 8

STEP 9

Now we have the answer in proper scientific notation.The correct answer is 2.8×10−72.8 \times 10^{-7}2.8×10−7.

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Assumptions
1. We are given the division problem $\frac{2.38 \times 10^{-2}}{8.5 \times 10^{4}}$ .
2. We need to simplify the expression to find the quotient.
3. The quotient should be expressed in scientific notation.

Apply the rule from STEP_2 to the given problem.
$\frac{2.38 \times 10^{-2}}{8.5 \times 10^{4}} = \frac{2.38}{8.5} \times 10^{-2 - 4}$

Subtract the exponents of 10.
$10^{-2 - 4} = 10^{-6}$

Now we divide the coefficients.
$\frac{2.38}{8.5}$

Perform the division.
$\frac{2.38}{8.5} \approx 0.28$

Combine the result of the division of coefficients with the result of the subtraction of exponents.
$0.28 \times 10^{-6}$

Now we have the answer in proper scientific notation.
The correct answer is $2.8 \times 10^{-7}$ .