Converting a Number Less Than 1 to Engineering Notation
(KS3, Year 7)

The Lesson

A number can be written in engineering notation. Imagine we wanted to write 0.0123 in engineering notation.

How to Convert a Number Less Than 1 to Engineering Notation

Converting a number less than 1 to engineering notation is easy.

Question

What is 0.0123 in engineering notation?

Step-by-Step:

1

Move the decimal point 3 places to the right.

0.012.3 Is there at least 1 but no more than 3 digits to the left of the decimal point (that are not 0s) now that it has been moved? Yes. There are 2 digits to the left of the new decimal point:

0.012.3 Note: If there are more than 3 digits to the left of the new decimal point, move the decimal point another 3 places to the right, and another, until there are between 1 and 3 digits to the left of the decimal point.

2

Ignore the 0s before the first non-0 digit.

12.3 12.3 will appear in the answer.

3

Count how many places the decimal point has been moved right. In our example, the decimal point has been moved 3 places to the right.

1The decimal point has mo

4

Take the negative of the answer to Step 3. The negative of 3 is −3.

5

Make the answer to Step 4 (−3) the exponent of a power of 10.

10 to the minus 3 10−3 will appear in the answer.

6

The number in engineering notation will consist of the number between 1 and 1,000 found in Step 2 (12.3) multiplying the power of 10 found in Step 5 (10−3).

Answer:

We have converted the number less than 1 to engineering notation:

12.3 times 10 to the minus 3

Lesson Slides

The slider below gives a real example of converting a number less than 1 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?