Multiplying and Dividing in Scientific Notation

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Question 1 of 5

1. Question
Multiply

$(4.0xx 10^5)(3.2xx10^(-3))$

Provide your answer in numerical notation
- (1280)
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Scientific notation is a way to represent very large or very small numbers in a compact form. It is in the format: $a xx 10^n$ .

Multiply the numbers first and then the exponents of $10$ separately.

$($ $4.0$ $xx$ $10^5$ $)($ $3.2$ $xx$ $10^(-3)$ $)$

$4.0$ $xx$ $3.2$ $=$ $12.8$

$(10^5)$ $xx$ $(10^(-3))$ $=$ $10^2$ Multiplication property of exponents

Combine the obtained values and simplify.

$12.8$ $xx$ $10^2$ $=$ $1.28xx 10^3$ Move the decimal point one place to the left

$=$ $1280$ Express in numerical notation

$1280$
Question 2 of 5

2. Question
Divide

$(3.5xx 10^(-7))/(7.0xx10^5)$
- 1. $5 xx 10^(-14)$
- 2. $5 xx 10^(-13)$
- 3. $5 xx 10^(-10)$
- 4. $5 xx 10^(-12)$
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Scientific notation is a way to represent very large or very small numbers in a compact form. It is in the format: $a xx 10^n$ .

Divide the numbers first and then the exponents of $10$ separately.

$\frac{\color\green{3.5} \times \color{#004ec4}{10^{-7}}}{\color\green{7.0} \times \color{#004ec4}{10^5}}$

$3.5/7.0$ $=$ $0.5$

$(10^(-7))/(10^5)$ $=$ $10^(-7-5)$ $=$ $10^(-12)$ Division property of exponents

Combine the obtained values and simplify.

$0.5$ $xx$ $10^(-12)$ $=$ $5xx 10^(-13)$ Move the decimal point one place to the right

$5 xx 10^(-13)$
Question 3 of 5

3. Question
Divide

$((7.5xx 10^(-4))(3.2 xx 10^5))/(3.75xx10^9)$

Provide your answer in numerical notation
- (0.000000064)
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Scientific notation is a way to represent very large or very small numbers in a compact form. It is in the format: $a xx 10^n$ .

Multiply and divide the numbers first and then the exponents of $10$ separately.

$\frac{(\color\green{7.5} \times \color{#004ec4}{10^{-4}})(\color\green{3.2} \times \color{#004ec4}{10^5})}{\color\green{3.75} \times \color{#004ec4}{10^9}}$

$(7.5xx3.2)/3.75$ $=$ $6.4$

$((10^(-4))xx10^5)/(10^9)$ $=$ $(10^(-4+5))/(10^9)$ $=$ $(10^1)/(10^9)$ $=$ $10^(-8)$ Multiplication and Division property of exponents

Combine the obtained values and simplify.

$6.4$ $xx$ $10^(-8)$ $=$ $0.000000064$ Express in numerical notation

$0.000000064$
Question 4 of 5

4. Question
Multiply

$0.0064 xx 0.0000071$
- 1. $4.544 xx 10^8$
- 2. $4.544 xx 10^9$
- 3. $4.544 xx 10^(-9)$
- 4. $4.544 xx 10^(-8)$
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Scientific notation is a way to represent very large or very small numbers in a compact form. It is in the format: $a xx 10^n$ .

Convert the numbers into scientific notation.

$0.0064$ $=$ $6.4 xx 10^(-3)$ Move the decimal point $3$ places to the right

$0.0000071$ $=$ $7.1 xx 10^(-6)$ Move the decimal point $6$ places to the right

Multiply the numbers first and then the exponents of $10$ separately.

$($ $6.4$ $xx$ $10^(-3)$ $)($ $7.1$ $xx$ $10^(-6)$ $)$

$6.4$ $xx$ $7.1$ $=$ $45.44$

$(10^(-3))$ $xx$ $(10^(-6))$ $=$ $10^(-9)$ Multiplication property of exponents

Combine the obtained values and simplify.

$45.44$ $xx$ $10^(-9)$ $=$ $4.544 xx 10^(-8)$ Move the decimal point one place to the left

$4.544 xx 10^(-8)$
Question 5 of 5

5. Question
Multiply

$0.032 xx 580000$
- 1. $1.856 xx 10^4$
- 2. $1.856 xx 10^2$
- 3. $1.856 xx 10^3$
- 4. $1.856 xx 10^(-4)$
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Scientific notation is a way to represent very large or very small numbers in a compact form. It is in the format: $a xx 10^n$ .

Convert the numbers into scientific notation.

$0.032$ $=$ $3.2 xx 10^(-2)$ Move the decimal point $2$ places to the right

$580000$ $=$ $5.8 xx 10^5$ Move the decimal point $5$ places to the left

Multiply the numbers first and then the exponents of $10$ separately.

$($ $3.2$ $xx$ $10^(-2)$ $)($ $5.8$ $xx$ $10^5$ $)$

$3.2$ $xx$ $5.8$ $=$ $18.56$

$(10^(-2))$ $xx$ $(10^5)$ $=$ $10^3$ Multiplication property of exponents

Combine the obtained values and simplify.

$18.56$ $xx$ $10^3$ $=$ $1.856 xx 10^4$ Move the decimal point one place to the left

$1.856 xx 10^4$

Multiplying and Dividing in Scientific Notation

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Quiz summary

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1. Question

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2. Question

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3. Question

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4. Question

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5. Question

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Quizzes

$4.0$ $xx$ $3.2$ $=$ $12.8$
$(10^5)$ $xx$ $(10^(-3))$ $=$ $10^2$			Multiplication property of exponents

$12.8$ $xx$ $10^2$	$=$	$1.28xx 10^3$	Move the decimal point one place to the left
	$=$	$1280$	Express in numerical notation

$3.5/7.0$ $=$ $0.5$
$(10^(-7))/(10^5)$ $=$ $10^(-7-5)$ $=$ $10^(-12)$			Division property of exponents

$(7.5xx3.2)/3.75$ $=$ $6.4$
$((10^(-4))xx10^5)/(10^9)$ $=$ $(10^(-4+5))/(10^9)$ $=$ $(10^1)/(10^9)$ $=$ $10^(-8)$			Multiplication and Division property of exponents

$0.0064$	$=$	$6.4 xx 10^(-3)$	Move the decimal point $3$ places to the right
$0.0000071$	$=$	$7.1 xx 10^(-6)$	Move the decimal point $6$ places to the right

$6.4$ $xx$ $7.1$ $=$ $45.44$
$(10^(-3))$ $xx$ $(10^(-6))$ $=$ $10^(-9)$			Multiplication property of exponents

$0.032$	$=$	$3.2 xx 10^(-2)$	Move the decimal point $2$ places to the right
$580000$	$=$	$5.8 xx 10^5$	Move the decimal point $5$ places to the left

$3.2$ $xx$ $5.8$ $=$ $18.56$
$(10^(-2))$ $xx$ $(10^5)$ $=$ $10^3$			Multiplication property of exponents