# How to Convert Engineering Notation with a Negative Exponent

## Converting Engineering Notation with a Negative Exponent

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. We have taken the number written in engineering notation and written it in full:

1.23 × 10−3 = 0.00123

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