The Lesson

A number can be written in scientific notation. Imagine we wanted to write 0.00123 in scientific notation.

How to Convert a Number Less Than 1 to Scientific Notation

Converting a number less than 1 to scientific notation is easy.

Question

What is 0.00123 in scientific notation?

Step-by-Step:

1

Place a new decimal point to the right of the first non-0 digit of the number. In our example, the first non-0 digit of 0.00123 is 1: 0.001.23

2

Ignore the 0s before the first non-0 digit. 1.23 1.23 will appear in the answer.

3

Count how many digits there are between the old and the new decimal point. (Don't ignore the 0s before the first non-0 digit this time). 0.001.23 There are 3 digits between the old and the new decimal point.

4

Take the negative of the answer to Step 3. The negative of 3 is −3.

5

Make the answer to Step 4 (−3) the exponent of a power of 10. 10 to the minus 3 10−3 will appear in the answer.

6

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 5 (10−3).

Answer:

We have converted the number less than 1 to scientific notation: 1.23 times 10 to the minus 3

Lesson Slides

The slider below gives a real example of converting a number less than 1 to scientific notation.

An Intuitive Method for Converting a Number to Scientific Notation

Consider the example of writing 0.00123 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 0.00123 in scientific notation, we wish to write our number (0.00123) with a decimal point after the first non-0 digit (1.23) multiplied by a power of 10. 1.23 times 10 to the power of ? The decimal point must be moved from after the first digit (0.00123) to after the first non-0 digit (0001.23). It needs to be moved a number of places to the right. We can see it needs to move 3 places to the right. The decimal point is moved 3 places to the right It is the power of 10 that moves the decimal point to the right. The exponent of the power of 10 must be the same as the number of places that the decimal point has moved right. But, it must be negative because a positive exponent moves the decimal point to the left. Since the decimal point has moved 3 places to the right, the exponent of the power of 10 is −3. 1.23 times 10 to the minus 3