Mathematics-Monster.com
(#mm)

menu

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

homenotationconverting a number less than 1 to engineering notation
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.

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...
author logo

This page was written by Stephen Clarke.

You might also like...

Help Us Improve Mathematics Monster

  • Do you disagree with something on this page?
  • Did you spot a typo?
Please tell us using this form.

Find Us Quicker!

  • When using a search engine (e.g., Google, Bing), you will find Mathematics Monster quicker if you add #mm to your search term.

Share This Page

share icon

If you like Grammar Monster (or this page in particular), please link to it or share it with others.

If you do, please tell us. It helps us a lot!

Create a QR Code

create QR code

Use our handy widget to create a QR code for this page...or any page.