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).
StepbyStep:
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