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?
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.

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.

    .1.23
  • To move the full 3 places, we need to write 0s in the next 2 places.

    .001.23

4

Write a 0 before the decimal point.

0.00123

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. Open the slider in a new tab

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".

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, 102 is a power of 10.

10 squared. The base is 10. The exponent is 2. 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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See Also

What is a power? What is a base? What is an exponent? What is scientific notation?