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Converting Scientific Notation with a Negative Exponent

(KS3, Year 7)

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?

In scientific notation, a number between 1 and 10 (1.23 in this example) is multiplied by a power of 10 (10⁻³ in this example). 1.23 times 10 to the minus 3 explained

Step-by-Step:

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. 1 decimal point 23

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.

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

Lesson Slides

The slider below gives a real example of converting scientific notation with a negative exponent.

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".