Solved on Feb 02, 2024

Divide $8.8 \times 10^{-3}$ by $2.4 \times 10^{-7}$ and give the answer in scientific notation.

STEP 1

Assumptions
1. We are given two numbers in scientific notation: $8.8 \times 10^{-3}$ and $2.4 \times 10^{-7}$ .
2. We need to divide these two numbers.
3. The result should be expressed in standard scientific notation.

STEP 2

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

STEP 3

First, divide the coefficients $8.8$ by $2.4$ .
$\frac{8.8}{2.4}$

STEP 4

Calculate the division of the coefficients.
$\frac{8.8}{2.4} = 3.666\ldots \approx 3.7 \text{ (rounded to two significant figures)}$

STEP 5

Now, subtract the exponent of the divisor $-7$ from the exponent of the dividend $-3$ .
$-3 - (-7) = -3 + 7$

STEP 6

Calculate the exponent after subtraction.
$-3 + 7 = 4$

STEP 7

Combine the result from STEP_4 and STEP_6 to express the final answer in standard scientific notation.
$3.7 \times 10^{4}$
The answer is $3.7 \times 10^{4}$ .

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Divide $8.8 \times 10^{-3}$ by $2.4 \times 10^{-7}$ and give the answer in scientific notation.

STEP 1

Assumptions
1. We are given two numbers in scientific notation: $8.8 \times 10^{-3}$ and $2.4 \times 10^{-7}$ .
2. We need to divide these two numbers.
3. The result should be expressed in standard scientific notation.

STEP 2

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

STEP 3

First, divide the coefficients $8.8$ by $2.4$ .
$\frac{8.8}{2.4}$

STEP 4

Calculate the division of the coefficients.
$\frac{8.8}{2.4} = 3.666\ldots \approx 3.7 \text{ (rounded to two significant figures)}$

STEP 5

Now, subtract the exponent of the divisor $-7$ from the exponent of the dividend $-3$ .
$-3 - (-7) = -3 + 7$

STEP 6

Calculate the exponent after subtraction.
$-3 + 7 = 4$

STEP 7

Combine the result from STEP_4 and STEP_6 to express the final answer in standard scientific notation.
$3.7 \times 10^{4}$
The answer is $3.7 \times 10^{4}$ .

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Divide 8.8×10−38.8 \times 10^{-3}8.8×10−3 by 2.4×10−72.4 \times 10^{-7}2.4×10−7 and give the answer in scientific notation.

STEP 1

Assumptions1. We are given two numbers in scientific notation: 8.8×10−38.8 \times 10^{-3}8.8×10−3 and 2.4×10−72.4 \times 10^{-7}2.4×10−7.2. We need to divide these two numbers.3. The result should be expressed in standard scientific notation.

STEP 2

STEP 3

First, divide the coefficients 8.88.88.8 by 2.42.42.4.8.82.4 \frac{8.8}{2.4} 2.48.8​

STEP 4

Calculate the division of the coefficients.8.82.4=3.666…≈3.7 (rounded to two significant figures) \frac{8.8}{2.4} = 3.666\ldots \approx 3.7 \text{ (rounded to two significant figures)} 2.48.8​=3.666…≈3.7 (rounded to two significant figures)

STEP 5

Now, subtract the exponent of the divisor −7-7−7 from the exponent of the dividend −3-3−3.−3−(−7)=−3+7 -3 - (-7) = -3 + 7 −3−(−7)=−3+7

STEP 6

Calculate the exponent after subtraction.−3+7=4 -3 + 7 = 4 −3+7=4

STEP 7

Combine the result from STEP_4 and STEP_6 to express the final answer in standard scientific notation.3.7×104 3.7 \times 10^{4} 3.7×104The answer is 3.7×1043.7 \times 10^{4}3.7×104.

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Divide $8.8 \times 10^{-3}$ by $2.4 \times 10^{-7}$ and give the answer in scientific notation.

Assumptions
1. We are given two numbers in scientific notation: $8.8 \times 10^{-3}$ and $2.4 \times 10^{-7}$ .
2. We need to divide these two numbers.
3. The result should be expressed in standard scientific notation.

First, divide the coefficients $8.8$ by $2.4$ .
$\frac{8.8}{2.4}$

Calculate the division of the coefficients.
$\frac{8.8}{2.4} = 3.666\ldots \approx 3.7 \text{ (rounded to two significant figures)}$

Now, subtract the exponent of the divisor $-7$ from the exponent of the dividend $-3$ .
$-3 - (-7) = -3 + 7$

Calculate the exponent after subtraction.
$-3 + 7 = 4$

Combine the result from STEP_4 and STEP_6 to express the final answer in standard scientific notation.
$3.7 \times 10^{4}$
The answer is $3.7 \times 10^{4}$ .