^{-3}represents.

## How to Convert Engineering Notation with a Negative Exponent

Converting engineering notation with a negative exponent to a number is easy.## Question

What is 1.23 × 10^{−3}written in full?

^{−3}in this example).

## Step-by-Step:

## 1

Look at the number between 1 and 1,000. In our example, the number between 1 and 1,000 is 1.23.
Find the decimal point in the number between 1 and 1,000.

**Don't forget:**If the number does not have a decimal point written, it can be written at the end of the number with a 0 after it (1 = 1.0).## 2

Find the exponent of the power of 10. In our example, the exponent of the power of 10 is

**−3**.## 3

Move the decimal point found in

**Step 1**by the number of places given by the exponent in**Step 2**. In our example, we will move the decimal places**3**places. Because it is**minus**3, the decimal point will be moved to the**left**.- When we move the decimal point 1 place to the left, we come past the first digit in the number.
- To move the full 3 places, we need to write
**0**s in the next 2 places.

## 3

Write a

**0**before the decimal point.## Answer:

We have taken the number written in engineering notation and written it in full:
1.23 × 10

^{−3}= 0.00123## 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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