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# Converting a Number to Scientific Notation

(KS3, Year 7)

## The Lesson

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**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).

There are

There are

**5**digits after the first digit.# 4

# 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**(10^{5}).## Answer:

We have converted the 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**.

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**.

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