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Converting a Number to Scientific Notation

(KS3, Year 7)

A number can be written in scientific notation. Imagine we wanted to write 123,000 in scientific notation.

How to Convert a Number to Scientific Notation

Converting a number to scientific notation is easy.

Question

What is 123,000 in scientific notation?

Step-by-Step:

1

Place a decimal point to the right of the first digit of the number. In our example, the first digit of 123,000 is 1:

2

Ignore the 0s after the last non-0 digit. 1.23

1.23 will appear in the answer.

3

Count how many digits there are after the first digit. (Don't ignore the 0s after the last non-0 digit this time). 1 point 23000 has 5 digits after the decimal point

1 point 23000 has 5 digits after the decimal point

There are 5 digits after the first digit.

4

Make the answer to Step 3 (5) the exponent of a power of 10.

10⁵ will appear in the answer.

5

The number in scientific notation will consist of the number between 1 and 10 found in Step 2 (1.23) multiplying the power of 10 found in Step 4 (10⁵).

Answer:

We have converted the number to scientific notation: 1.23 times 10 to the 5

Lesson Slides

The slider below gives a real example of converting a number to scientific notation.

An Intuitive Method for Converting a Number to Scientific Notation

Consider the example of writing 123,000 in scientific notation. A number written in scientific notation consists of a number between 1 and 10 multiplying a power of 10. To write the 123,000 in scientific notation, we wish to write our number (123,000) with a decimal point after the first digit (1.23) multiplied by a power of 10.

Even though it is not written, there is a decimal point after the last digit (the last 0 in 123,000). It needs to be moved a number of places to the left so that it is after the first digit (the 1 in 123,000). We can see it needs to move 5 places to the left. The decimal point is moved 5 places to the left

The decimal point is moved 5 places to the left

It is the power of 10 that moves the decimal point to the left. The exponent of the power of 10 must be the same as the number of places that the decimal point has moved left. Since the decimal point has moved 5 places to the left, the exponent of the power of 10 is 5. 1.23 times 10 to the 5