Multiplying and Dividing in Scientific Notation

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Question 1 of 5

1. Question
Multiply

$(4.0 \times 10^{5}) (3.2 \times 10^{- 3})$ $(4.0xx 10^5)(3.2xx10^(-3))$

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: $a \times 10^{n}$ $a xx 10^n$ .

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

$($ $($ $4.0$ $4.0$ $\times$ $xx$ $10^{5}$ $10^5$ $) ($ $)($ $3.2$ $3.2$ $\times$ $xx$ $10^{- 3}$ $10^(-3)$ $)$ $)$

$4.0$ $4.0$ $\times$ $xx$ $3.2$ $3.2$ $=$ $=$ $12.8$ $12.8$

$(10^{5})$ $(10^5)$ $\times$ $xx$ $(10^{- 3})$ $(10^(-3))$ $=$ $=$ $10^{2}$ $10^2$ Multiplication property of exponents

Combine the obtained values and simplify.

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

$=$ $=$ $1280$ $1280$ Express in numerical notation

$1280$ $1280$
Question 2 of 5

2. Question
Divide

$\frac{3.5 \times 10^{- 7}}{7.0 \times 10^{5}}$ $(3.5xx 10^(-7))/(7.0xx10^5)$
- 1. $5 \times 10^{- 13}$ $5 xx 10^(-13)$
- 2. $5 \times 10^{- 10}$ $5 xx 10^(-10)$
- 3. $5 \times 10^{- 14}$ $5 xx 10^(-14)$
- 4. $5 \times 10^{- 12}$ $5 xx 10^(-12)$
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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: $a \times 10^{n}$ $a xx 10^n$ .

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

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

$\frac{3.5}{7.0}$ $3.5/7.0$ $=$ $=$ $0.5$ $0.5$

$\frac{10^{- 7}}{10^{5}}$ $(10^(-7))/(10^5)$ $=$ $=$ $10^{- 7 - 5}$ $10^(-7-5)$ $=$ $=$ $10^{- 12}$ $10^(-12)$ Division property of exponents

Combine the obtained values and simplify.

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

$5 \times 10^{- 13}$ $5 xx 10^(-13)$

Question 3 of 5

Divide

\frac{(7.5 \times 10^{- 4}) (3.2 \times 10^{5})}{3.75 \times 10^{9}}

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

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 \times 10^{n}

$a xx 10^n$ .

Multiply and divide the numbers first and then the exponents of

10

$10$ separately.

\frac{(7.5 \times 10^{- 4}) (3.2 \times 10^{5})}{3.75 \times 10^{9}}

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

$\frac{7.5 \times 3.2}{3.75}$ $(7.5xx3.2)/3.75$ $=$ $=$ $6.4$ $6.4$
$\frac{(10^{- 4}) \times 10^{5}}{10^{9}}$ $((10^(-4))xx10^5)/(10^9)$ $=$ $=$ $\frac{10^{- 4 + 5}}{10^{9}}$ $(10^(-4+5))/(10^9)$ $=$ $=$ $\frac{10^{1}}{10^{9}}$ $(10^1)/(10^9)$ $=$ $=$ $10^{- 8}$ $10^(-8)$			Multiplication and Division property of exponents

Combine the obtained values and simplify.

$6.4$ $6.4$

\times

$xx$ $10^{- 8}$ $10^(-8)$

=

$=$

0.000000064

$0.000000064$

Express in numerical notation

0.000000064

$0.000000064$

Question 4 of 5

Multiply

0.0064 \times 0.0000071

$0.0064 xx 0.0000071$

1. $4.544 \times 10^{8}$ $4.544 xx 10^8$
2. $4.544 \times 10^{- 8}$ $4.544 xx 10^(-8)$
3. $4.544 \times 10^{- 9}$ $4.544 xx 10^(-9)$
4. $4.544 \times 10^{9}$ $4.544 xx 10^9$

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

$1.856 xx 10^4$

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

Multiplying and Dividing in Scientific Notation

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Quiz summary

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Quizzes

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

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

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

$6.4$ $6.4$ $\times$ $xx$ $7.1$ $7.1$ $=$ $=$ $45.44$ $45.44$
$(10^{- 3})$ $(10^(-3))$ $\times$ $xx$ $(10^(-6))$ $=$ $10^(-9)$			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