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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?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).
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
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
Powers of 10
A power of 10 is 10 raised to a exponent. For example, 10^{3} 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.
10^{3} = 10 × 10 × 10
The answer will have 3 0s after the 1:
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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