Solved on Dec 05, 2023

Evaluate the quotient $\left(5.44 \times 10^{-18}\right) \div\left(6.8 \times 10^{-9}\right)$ and express the result in scientific notation.

STEP 1

Assumptions
1. We are given two numbers in scientific notation: $5.44 \times 10^{-18}$ and $6.8 \times 10^{-9}$ .
2. We need to divide these two numbers.
3. The result 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 $10$ ) and subtract the exponent of the divisor from the exponent of the dividend.
$\frac{a \times 10^n}{b \times 10^m} = \frac{a}{b} \times 10^{n-m}$

STEP 3

Now, we will apply this rule to the given numbers.
$\frac{5.44 \times 10^{-18}}{6.8 \times 10^{-9}} = \frac{5.44}{6.8} \times 10^{-18 - (-9)}$

STEP 4

First, we divide the coefficients.
$\frac{5.44}{6.8} = 0.8$

STEP 5

Next, we subtract the exponents.
$-18 - (-9) = -18 + 9 = -9$

STEP 6

Now, we combine the results of the coefficient division and the exponent subtraction.
$0.8 \times 10^{-9}$

STEP 7

The result is already in scientific notation, so we can conclude that:
$\left(5.44 \times 10^{-18}\right) \div\left(6.8 \times 10^{-9}\right) = 0.8 \times 10^{-9}$

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Evaluate the quotient $\left(5.44 \times 10^{-18}\right) \div\left(6.8 \times 10^{-9}\right)$ and express the result in scientific notation.

STEP 1

Assumptions
1. We are given two numbers in scientific notation: $5.44 \times 10^{-18}$ and $6.8 \times 10^{-9}$ .
2. We need to divide these two numbers.
3. The result 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 $10$ ) and subtract the exponent of the divisor from the exponent of the dividend.
$\frac{a \times 10^n}{b \times 10^m} = \frac{a}{b} \times 10^{n-m}$

STEP 3

Now, we will apply this rule to the given numbers.
$\frac{5.44 \times 10^{-18}}{6.8 \times 10^{-9}} = \frac{5.44}{6.8} \times 10^{-18 - (-9)}$

STEP 4

First, we divide the coefficients.
$\frac{5.44}{6.8} = 0.8$

STEP 5

Next, we subtract the exponents.
$-18 - (-9) = -18 + 9 = -9$

STEP 6

Now, we combine the results of the coefficient division and the exponent subtraction.
$0.8 \times 10^{-9}$

STEP 7

The result is already in scientific notation, so we can conclude that:
$\left(5.44 \times 10^{-18}\right) \div\left(6.8 \times 10^{-9}\right) = 0.8 \times 10^{-9}$

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Evaluate the quotient (5.44×10−18)÷(6.8×10−9)\left(5.44 \times 10^{-18}\right) \div\left(6.8 \times 10^{-9}\right)(5.44×10−18)÷(6.8×10−9) and express the result in scientific notation.

STEP 1

Assumptions1. We are given two numbers in scientific notation: 5.44×10−185.44 \times 10^{-18}5.44×10−18 and 6.8×10−96.8 \times 10^{-9}6.8×10−9.2. We need to divide these two numbers.3. The result should be expressed in scientific notation.

STEP 2

STEP 3

Now, we will apply this rule to the given numbers.5.44×10−186.8×10−9=5.446.8×10−18−(−9) \frac{5.44 \times 10^{-18}}{6.8 \times 10^{-9}} = \frac{5.44}{6.8} \times 10^{-18 - (-9)} 6.8×10−95.44×10−18​=6.85.44​×10−18−(−9)

STEP 4

First, we divide the coefficients.5.446.8=0.8 \frac{5.44}{6.8} = 0.8 6.85.44​=0.8

STEP 5

Next, we subtract the exponents.−18−(−9)=−18+9=−9 -18 - (-9) = -18 + 9 = -9 −18−(−9)=−18+9=−9

STEP 6

Now, we combine the results of the coefficient division and the exponent subtraction.0.8×10−9 0.8 \times 10^{-9} 0.8×10−9

STEP 7

The result is already in scientific notation, so we can conclude that:(5.44×10−18)÷(6.8×10−9)=0.8×10−9 \left(5.44 \times 10^{-18}\right) \div\left(6.8 \times 10^{-9}\right) = 0.8 \times 10^{-9} (5.44×10−18)÷(6.8×10−9)=0.8×10−9

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Evaluate the quotient $\left(5.44 \times 10^{-18}\right) \div\left(6.8 \times 10^{-9}\right)$ and express the result in scientific notation.

Assumptions
1. We are given two numbers in scientific notation: $5.44 \times 10^{-18}$ and $6.8 \times 10^{-9}$ .
2. We need to divide these two numbers.
3. The result should be expressed in scientific notation.

Now, we will apply this rule to the given numbers.
$\frac{5.44 \times 10^{-18}}{6.8 \times 10^{-9}} = \frac{5.44}{6.8} \times 10^{-18 - (-9)}$

First, we divide the coefficients.
$\frac{5.44}{6.8} = 0.8$

Next, we subtract the exponents.
$-18 - (-9) = -18 + 9 = -9$

Now, we combine the results of the coefficient division and the exponent subtraction.
$0.8 \times 10^{-9}$

The result is already in scientific notation, so we can conclude that:
$\left(5.44 \times 10^{-18}\right) \div\left(6.8 \times 10^{-9}\right) = 0.8 \times 10^{-9}$