Scientific Notation Word Problems

Topics

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

39000000000000 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. $3.9 \times 10^{- 16} m$ $3.9xx10^(-16) m$
4. $3.9 \times 10^{15} m$ $3.9xx10^(15) m$

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 $778000000000 m$ $778 000 000 000 m$ .
- (2593) seconds
Hint

Help Video
Correct

Correct!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Formula for time

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

Label Known Values

Distance $= d = 778000000000 m$ $= d = 778 000 000 000 m$

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

Convert the distance into scientific notation.

$778000000000 m$ $778 000 000 000 m$ $=$ $=$ $7.78 \times 10^{11} m$ $7.78 xx 10^(11) m$ 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
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

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

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

$=$ $1.1 10^(-8) m$ 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

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