Engineering Notation
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This material was developed with funding from the
National Science Foundation under Grant # DUE 1601612
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1 ZETTA OR 1Z
1 x 1021
1000000000000000000000
1 MEGA OR 1M
1 x 106
1000000
1 atto OR 1a
1 x 10-18
0.000000000000000001
1 GIGA OR 1G
1 x 109
1000000000
Engineering Notation Units
1 TERA OR 1T
1 x 1012
1000000000000
1 milli OR 1m
1 x 10-3
0.001
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Drag the yellow arrow.
Engineering notation is a method of presenting very large and very small numbers in a simpler format. Engineering notation is like scientific notation, but the power of ten can only be a multiple of 3 (103, 10-6, 1015). Engineering notation follows the metric system prefixed names such as kilo (103), mega (106), giga (109), and nano (10-9).
1 PETA OR 1P
1 x 1015
1000000000000000
1 pico OR 1p
1 x 10-12
0.000000000001
1 KILO OR 1K
1 x 103
1000
1 micro OR 1μ
1 x 10-6
0.000001
1 zepto OR 1z
1 x 10-21
0.000000000000000000001
1 EXA OR 1E
1 x 1018
1000000000000000000
1 femto OR 1f
1 x 10-15
0.000000000000001
1 nano OR 1n
1 x 10-9
0.000000001
Click to reveal the examples
Examples of Engineering Notation
Very Large Values
What is engineering
notation?
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When you reference a number in millions, billions, or trillions, you are using engineering notation. Another way to think about it is in terms of commas placed in numbers to distinguish hundreds from thousands, thousands from millions, or millions from billions.
Very Small Values
Click to
view
Write the new number, and multiply it by base ten of the exponent.
3
Look up the engineering unit equivalent of the exponent value.
4
6
12.5 x
5
Move the decimal point to the left by three moves until three or less integers are to the left side of the decimal point. Each movement of three represents a new engineering notation unit.
9
12.5 Giga
This count represents the exponent.
2
Step 5
Counter = Exponent
Moving decimal left = Positive
Kilo
Number of hops
Click to
view
Mega
Step 3
Giga
10
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Step 4
Place a decimal point after the last digit on the right.
To convert very large numbers to engineering notation:
Converting Very Large Numbers
1
Step 1
Step 2
Write the coefficient and multiply it by base ten of the exponent.
Units
micro
4
Counter = Exponent
Moving decimal right = negative
nano
milli
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-9
Move the decimal point by three positions to the right until there are three or less digits to the right of the decimal point.
Record the count that the decimal point moved. This count represents the exponent.
Converting Very Small Numbers
-6
To convert very small numbers to engineering notation:
23.5 x
23.5 nano
-3
0
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Click to move decimal point 3 places to the left
Numbers in Engineering Notation
57.1 x 10
57.1 Mega
Decimal
Point
<
Click to add
decimal point
Click the buttons to move the decimal point to see how a value can be expressed in various engineering notation units.
The checkmark represents the number in its simplest form.
Move to Right (+)
0.000075
Move to Left (–)
75,000
Identify Engineering
Notation Units
75,000,000,000
75
75,000,000
75,000,000,000,000
75,000,000,000,000,000
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0.075
Engineering Notation Challenge 1
95,700,000
Original Number in Bytes
5,750,000,000
New Number in common EN MEGA
44,200,000,000
M
M
M
Element
with Audio
HTML
There are instances when you may need to covert numbers to a specific engineering notation (EN) unit.
M
6,320,000,000,000
M
Convert the following to a common EN MEGA
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22,750,000,000,000
M
132,000,000
G
G
Convert all the numbers to a common EN GIGA
Engineering Notation Challenge 3
G
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New Number in common EN GIGA
G
G
G
0.625
0.000000000000000000625
0.000625
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0.000000000000000625
0.000000000000625
625,000
625
0.000000000625
0.000000625
PETA
Drop unit
here
GIGA
5.75
6.32
132
44.2
Great Job!
New Number in EN
95.7
2.2
44,200
Mastering Engineering Notation 1
TERA
Drag and drop the correct engineering notation unit
MEGA
95,700,000,000,000,000,000
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KILO
ZETTA
2,200,000,000,000,000
22,750
6,320,000
132,000,000,000,000,000,000,000
Engineering Notation Challenge 2
5,750,000
95,700,000,000,000
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22,750,000,000,000,000,000
micro
87.5
0.0000000000001255
0.00725
0.0000875
62.5
0.00000000333
milli
pico
nano
7.25
2.25
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0.0000000000625
atto
Mastering Engineering Notation 2
0.00000000000000000225
3.33
125.5
femto
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0.0875
3,330
7,250
0.0000000000000000625
0.00225
Engineering Notation Challenge 4
0.00000000000225
micro
micro
0.000000000000125
micro
micro
micro
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Engineering Notation Challenge 5
New Number in common EN micro
micro
Convert all the numbers to a common EN micro
nano
Engineering Notation Challenge 6
nano
nano
New Number in common EN nano
0.000000000125
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nano
0.00025
nano
0.0000000325
0.00000275
0.000000000000825
nano
0.00000000000925
Convert all the numbers to a common EN nano
START
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Move the decimal point to the right by the number shown in the exponent.
To convert engineering notation to long form:
Place the decimal point.
Engineering Notation to Conventional Long Form
Very Large Value
Hold each digit place with a zero.
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12
15
Move the decimal point to the left by the number shown in the exponent.
Engineering Notation to Conventional Long Form
Very Small Value
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-12
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24.5 PETA
125.0 KILO
Enter the long form of each Engineering Notation value below.
Mastering Converting From
Engineering Notation
7.33 TERA
26.25 MEGA
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2.75 GIGA
1.4 ZETTA
625.0 pico
125 micro
75.25 nano
5.25 milli
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Enter the long form of each engineering notation value below.
1.5 femto
75.25 Gigahertz or 75,250,000,000 or 75.25 x 109
5.25 Kilometers or 5,250 or 5.25 x 103
25.2 Megabytes or 25,200,000 or 25.2 x 106
1.25 millisecs or 0.00125 or 1.25 x 10-3
9.7 micrograms or 0.0000097 or 9.7 x 10-6
5.25 nanometers or 0.00000000525 or 5.25 x 10-9