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# 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.

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?

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:**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**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.# 4

# 5

# 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:## Powers of 10

A power of 10 is 10 raised to a exponent. For example,**10**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.

^{3}
10

The answer will have 3 0s after the 1:
^{3}= 10 × 10 × 10
10

^{3}= 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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