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Converting Scientific Notation with a Negative Exponent
(KS3, Year 7)
The Lesson
Scientific notation with a negative exponent is a way of writing small numbers. We need to know what number the scientific notation represents. Imagine we wanted to know what number 1.23 × 10^{3} represents.How to Convert Scientific Notation with a Negative Exponent
Converting scientific 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 10. In our example, the number between 1 and 10 is 1.23.
Find the decimal point in the number between 1 and 10.
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.
4
Write a 0 before the decimal point.
Answer:
We have taken the number written in scientific notation and written it in full:
1.23 × 10^{−3} = 0.00123
What Is Scientific Notation?
Scientific notation is a way of writing a number. In scientific notation, a number is written as a number between 1 and 10 multiplied by a power of 10. The number below is written in scientific notation. It is said as "1.2 times 10 to the 3".What Is a Power of 10?
A power of 10 is 10 raised to a exponent. For example, 10^{2} is a power of 10.The small 2 written beside the 10 means it is raised to an exponent of 2. This means 10 is multiplied by itself 2 times.
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