Engineering Notation
(KS3, Year 7)

The Lesson

Engineering notation is a way of writing a number. It is written as a number between 1 and 1,000 multiplied by a power of 10 that has an exponent that is a multiple of 3. The number below is written in engineering notation. It is said as "123.4 times 10 to the 3".

123.4 times 10 to the 3
  • 123.4 is between 1 and 1,000.
  • 103 is a power of 10. The exponent is 3, which is a multiple of 3. 106, 109 and 1012 also have exponents that are multiples of 3.

Understanding Engineering Notation

A number represented in engineering notation is written as a number between 1 and 1,000 multiplied by a power of 10 that is a multiple of 3. The power of 10 is written as a 10 with a raised number by its side. The raised number is called an exponent.

123.4 times 10 to the 6 It tells you how many times the 10 is multiplied by itself, or how many 0s there are after the 1.
123.4 × 103 = 123.4 × 10 × 10 × 10 = 123.4 × 1,000
So 123.4 × 103 represents the number given by 123.4 × 1000, which is 123,400.
123.4 × 103 = 123,400

Why Is Engineering Notation Useful?

Engineering notation is useful because it allows us to write very large or very small numbers in a shorter, standard way. Some examples of numbers written in engineering notation are shown below, along with the numbers written in full. Notice that it can save you writing lots of 0s.

4 times 10 to the 2 equals 200. 1.2 times 10 to the 5 equals 120,000 When numbers are very small (less than 1), we can also save writing 0s by using engineering notation. In this case, the power of 10 can has a negative exponent:

5.1 times 10 to the minus 2 equals 0.051

Converting a Number into Engineering Notation

Engineering notation is a useful way to write long numbers.

1,230,000 equals 1.23 times 10 to the 6 To convert the number to engineering notation, we have to move the decimal point left. Even though it isn't written, the decimal point is at the end of the number. It needs to move left by a multiple of 3 places. Keep moving left until there are at least 1, but no more than 3 digits to the left of the decimal point.

The decimal point needs to move 6 places to the left The decimal point has to be moved 6 places to the left to make 1.23. The number is written as 1.23 × 106.
Read more about converting numbers to engineering notation

Converting Engineering Notation to a Number

When you see a number written in engineering notation, you must know what number it represents.

1.23 times 10 to the 6 equals 1,230,000 To convert scientific notation to a number, we have to move the decimal point right. The exponent of the power of 10 is 6 so the decimal point needs to be moved 6 places. You will need to add 0s so that the decimal point can be moved:

The decimal point needs to move 6 places to the right The decimal point has to be moved 6 places to the right to make 1,230,000.
Read more about converting engineering notation to numbers

Lesson Slides

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Note

Number Between 1 and 1,000

The number in engineering notation (that multiplies the power of 10) is between 1 and 1,000. It can include 1, but not 1,000.

Powers of 10

A power of 10 is 10 raised to a exponent. For example, 103 is a power of 10. The small 3 written beside the 10 means it is raised to an exponent of 3. This means 10 is multiplied by itself 3 times.
103 = 10 × 10 × 10
The answer will have 3 0s after the 1:
103 = 1,000

What Is a Multiple of 3?

The exponent of the power of 10 in engineering notation must be a multiple of 3. A multiple of 3 is a number that results from multiplying 3 by a whole number. Multiples of 3 are:
3, 6, 9, 12, 15, 18, 21...
Multiples of 3 can be negative as well:
−3, −6, −9, −12, −15, −18, −21...

Other Ways of Writing Engineering Notation

To write engineering notation on a keyboard, the ^ symbol is used for the exponent of 10 (103 = 10^3):
5.2 × 103 = 5.2 × 10^3
On a calculator, the E symbol is used to represent a power of 10 (×102 = E2):
5.2 × 103 = 5.2E3

Scientific Notation

Scientific notation is similar to engineering notation, except the number is limited between 1 and 10, and the exponent of the power of 10 can be any whole number.
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See Also

What is a power? What is a base? What is an exponent? What is a power of 10? Negative exponents What is scientific notation?