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

10/24

0.0000000000625

atto

Mastering Engineering Notation 2

0.00000000000000000225

3.33

125.5

femto

22/24

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