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# Converting a Number Less Than 1 to Scientific Notation

(KS3, Year 7)

## 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:

# 2

Ignore the 0s before the first non-0 digit.

**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).

There are

There are

**3**digits between the old and the new decimal point.# 4

# 5

# 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:## 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.

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**.

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**.

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