Scientific Notation Word Problems

Years

Try VividMath Premium to unlock full access

Start Free Trial

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 4

The distance between Alpha Centauri and Earth is

39 000 000 000 000 k m

$39 000 000 000 000 km$ . Convert the distance into metres and express in scientific notation.

1. $3.9 \times 10^{16} m$ $3.9xx10^(16) m$
2. $3.9 \times 10^{13} m$ $3.9xx10^(13) m$
3. $3.9 \times 10^{15} m$ $3.9xx10^(15) m$
4. $3.9 \times 10^{- 16} m$ $3.9xx10^(-16) m$

Incorrect

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}

$a xx 10^n$ .

Use the conversion factor

1 k m = 1000 m

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

39 000 000 000 000 k m

$39 000 000 000 000 km$

=

$=$

39 000 000 000 000 000 m

$39 000 000 000 000 000 m$

Multipying by

1000

$1000$ is the same as adding

3

$3$ zeros

Write the obtained value in scientific notation.

39 000 000 000 000 000 m

$39 000 000 000 000 000 m$

=

$=$

3.9 \times 10^{16} m

$3.9xx 10^(16) m$

Move the decimal point

16

$16$ places to the left

3.9 \times 10^{16} m

$3.9xx10^(16) m$

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 $778 000 000 000 m$ $778 000 000 000 m$ .
- (2593) seconds
Hint

Help Video

Correct

Correct!

Incorrect

Formula for time

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

Label Known Values

Distance $= d = 778 000 000 000 m$ $= d = 778 000 000 000 m$

Speed $= s = 3 \times 10^{8} \frac{m}{s}$ $= s = 3 xx 10^8 m/s$

Convert the distance into scientific notation.

$778 000 000 000 m$ $778 000 000 000 m$ $=$ $=$ $7.78 \times 10^{11} m$ $7.78 xx 10^(11) m$ Move the decimal point $11$ $11$ 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 $10$ $10$ separately.

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

$\frac{7.78}{3}$ $7.78/3$ $=$ $=$ $2.593$ $2.593$

$\frac{10^{11}}{10^{8}}$ $(10^11)/(10^8)$ $=$ $=$ $10^{11 - 8}$ $10^(11-8)$ $=$ $=$ $10^{3}$ $10^3$ Division property of exponents

Combine the obtained values and simplify.

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

$2593$ $2593$ seconds
Question 3 of 4

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

Help Video

Correct

Keep Going!

Incorrect

Conversion of nanometres to metres

$1$ $1$ nanometre $= 1 \times 10^{- 9}$ $=1xx10^(-9)$ metre

Multiply the given value by the conversion factor.

$11$ $11$ nanometres $=$ $=$ $11 \times 1 \times 10^{- 9} m$ $11 xx 1 xx10^(-9) m$

$=$ $=$ $11 \times 10^{- 9} m$ $11 xx10^(-9) m$

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

Write the obtained value in numerical notation.

$1.1 \times 10^{- 8} m$ $1.1xx10^(-8) m$ $=$ $=$ $0.000000011 m$ $0.000000011 m$ Move the decimal point $8$ $8$ places to the left

$0.000000011 m$ $0.000000011 m$

Question 4 of 4

The diameter of a strand of hair is

50 000

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

(0.00005) $m$ $m$

Incorrect

Conversion of nanometres to metres

1

$1$ nanometre

= 1 \times 10^{- 9}

$=1xx10^(-9)$ metre

Multiply the given value by the conversion factor.

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

Write the obtained value in numerical notation.

5 \times 10^{- 5} m

$5xx10^(-5) m$

=

$=$

0.00005 m

$0.00005 m$

Move the decimal point

5

$5$ places to the left

0.00005 m

$0.00005 m$

Scientific Notation Word Problems

Try VividMath Premium to unlock full access

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

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

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

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