Scientific Notation Word Problems

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Question 1 of 4

1. Question
The distance between Alpha Centauri and Earth is $39 000 000 000 000 km$ . Convert the distance into metres and express in scientific notation.
- 1. $3.9xx10^(16) m$
- 2. $3.9xx10^(-16) m$
- 3. $3.9xx10^(13) m$
- 4. $3.9xx10^(15) m$
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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: $a xx 10^n$ .

Use the conversion factor $1 km = 1000 m$ to convert the distance into metres.

$39 000 000 000 000 km$ $=$ $39 000 000 000 000 000 m$ Multipying by $1000$ is the same as adding $3$ zeros

Write the obtained value in scientific notation.

$39 000 000 000 000 000 m$ $=$ $3.9xx 10^(16) m$ Move the decimal point $16$ places to the left

$3.9xx10^(16) m$
Question 2 of 4

2. Question
Find the time it takes light to travel from the Sun all the way to Jupiter, if the distance between them is $778 000 000 000 m$ .
- (2593) seconds
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Formula for time

$\color\red{t}=\frac {\color{#a300c1}{d}}{\color{#e85e00}{s}}$

Label Known Values

Distance $= d = 778 000 000 000 m$

Speed $= s = 3 xx 10^8 m/s$

Convert the distance into scientific notation.

$778 000 000 000 m$ $=$ $7.78 xx 10^(11) m$ Move the decimal point $11$ places to the left

Substitute the values into the formula

$\color\red{t}$ $=\frac {\color{#a300c1}{d}}{\color{#e85e00}{s}}$

$=\frac {\color{#a300c1}{7.78 \times 10^{11}}}{\color{#e85e00}{3 \times 10^{8}}}$

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

$\frac{\color\green{7.78} \times \color{#004ec4}{10^{11}}}{\color\green{3} \times \color{#004ec4}{10^8}}$

$7.78/3$ $=$ $2.593$

$(10^11)/(10^8)$ $=$ $10^(11-8)$ $=$ $10^3$ Division property of exponents

Combine the obtained values and simplify.

$2.593$ $xx$ $10^3$ $=$ $2593$ seconds Move the decimal point three places to the right

$2593$ seconds
Question 3 of 4

3. Question
The thickness of a thin film of a soap bubble is $11$ nanometres. Transform this into numerical notation and express in metres.
- (0.000000011) $m$
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Conversion of nanometres to metres

$1$ nanometre $=1xx10^(-9)$ metre

Multiply the given value by the conversion factor.

$11$ nanometres $=$ $11 xx 1 xx10^(-9) m$

$=$ $11 xx10^(-9) m$

$=$ $1.1 10^(-8) m$ Move one place to the left

Write the obtained value in numerical notation.

$1.1xx10^(-8) m$ $=$ $0.000000011 m$ Move the decimal point $8$ places to the left

$0.000000011 m$

Question 4 of 4

The diameter of a strand of hair is

$50 000$ nanometres. Transform this into numerical notation and express in metres.

(0.00005) $m$

$50 000$ nanometres	$=$	$50 000 xx 1 xx10^(-9) m$
	$=$	$5 xx 10^4 xx10^(-9) m$	Convert $50 000$ into scientific notation
	$=$	$5 xx10^(-9+4) m$	Apply Multiplication rule of exponents
	$=$	$5xx10^(-5) m$	Simplify

Scientific Notation Word Problems

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Quiz summary

Information

1. Question

Hint

Great Work!

2. Question

Hint

Correct!

Formula for time

Label Known Values

3. Question

Hint

Keep Going!

Conversion of nanometres to metres

4. Question

Hint

Fantastic!

Conversion of nanometres to metres

Quizzes

$\color\red{t}$	$=\frac {\color{#a300c1}{d}}{\color{#e85e00}{s}}$
	$=\frac {\color{#a300c1}{7.78 \times 10^{11}}}{\color{#e85e00}{3 \times 10^{8}}}$

$7.78/3$ $=$ $2.593$
$(10^11)/(10^8)$ $=$ $10^(11-8)$ $=$ $10^3$			Division property of exponents

$11$ nanometres	$=$	$11 xx 1 xx10^(-9) m$
	$=$	$11 xx10^(-9) m$
	$=$	$1.1 10^(-8) m$	Move one place to the left