# Converting Engineering Notation with a Negative Exponent(KS3, Year 7)

## The Lesson

Engineering notation with a negative exponent is a way of writing small numbers. We need to know what number the engineering notation represents. Imagine we wanted to know what number 1.23 × 10-3 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?
In engineering notation, a number between 1 and 1,000 (1.23 in this example) is multiplied by a power of 10 that has an exponent that is a multiple of 3 (10−3 in this example). # 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 0s 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

## Lesson Slides

The slider below gives a real example of converting engineering notation with a negative exponent. 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 negative exponent? What is a multiple?