Converting a Number to Engineering Notation
(KS3, Year 7)

The Lesson

A number can be written in engineering notation. Imagine we wanted to write 1,230,000 in engineering notation.

How to Convert a Number to Engineering Notation

Converting a number to engineering notation is easy.

Question

What is 1,230,000 in engineering notation?
To convert the number to engineering notation, we must move the decimal point from the end of the number to the left in groups of 3 places until there is at least 1 but no more than 3 digits to the left of the decimal point.

Step-by-Step:

1

Write the decimal point at the end of the number.

1,230,000.

2

Move the decimal point 3 places to the left.

1,230.000 Is there at least 1 but no more than 3 digits to the left of the decimal point? No. There are 4 digits to the left of the decimal point.

3

Move the decimal point another 3 places to the left.

1.230,000 Is there at least 1 but no more than 3 digits to the left of the decimal point? Yes. There is only 1 digit to the left of the decimal point.

4

Ignore the 0s after the last non-0 digit.

1.23 1.23 will appear in the answer.

5

Count how many places the decimal point has been moved left. In our example, the decimal point has been moved 6 places to the left.

The decimal place has been moved 6 places to the left

6

Make the answer to Step 5 (6) the exponent of a power of 10.

10 to the 6 106 will appear in the answer.

7

The number in engineering notation will consist of the number between 1 and 1,000 found in Step 4 (1.23) multiplying the power of 10 found in Step 6 (106).

Answer:

We have converted the number to engineering notation:

1.23 times 10 to the 6

Lesson Slides

The slider below gives a real example of converting a number to engineering notation. Open the slider in a new tab

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...
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See Also

What is a power? What is a base? What is an exponent? What is a power of 10? What is a multiple?