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# Converting a Number to Engineering Notation

(KS3, Year 7)

## The Lesson

A number can be written in engineering notation. Imagine we wanted to write 1,230,000 in engineering notation.## How to Convert a Number to Engineering Notation

Converting a number to engineering notation is easy.## Question

What is 1,230,000 in engineering notation?## Step-by-Step:

# 1

Write the decimal point at the end of the number.

# 2

Move the decimal point 3 places to the left.

Is there at least 1 but no more than 3 digits to the left of the decimal point?

Is there at least 1 but no more than 3 digits to the left of the decimal point?

**No**. There are 4 digits to the left of the decimal point.# 3

Move the decimal point another 3 places to the left.

Is there at least 1 but no more than 3 digits to the left of the decimal point?

Is there at least 1 but no more than 3 digits to the left of the decimal point?

**Yes**. There is only 1 digit to the left of the decimal point.# 4

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

**1.23**will appear in the answer.# 5

Count how many places the decimal point has been moved left. In our example, the decimal point has been moved

**6**places to the left.# 6

# 7

The number in engineering notation will consist of the number between 1 and 1,000 found in

**Step 4**(1.23) multiplying the power of 10 found in**Step 6**(10^{6}).## Answer:

We have converted the number to engineering notation:## Powers of 10

A power of 10 is 10 raised to a exponent. For example,**10**is a power of 10. The small 3 written beside the 10 means it is raised to an exponent of 3. This means 10 is multiplied by itself 3 times.

^{3}
10

The answer will have 3 0s after the 1:
^{3}= 10 × 10 × 10
10

^{3}= 1,000## What Is a Multiple of 3?

The exponent of the power of 10 in engineering notation must be a multiple of 3. A multiple of 3 is a number that results from multiplying 3 by a whole number. Multiples of 3 are:
3, 6, 9, 12, 15, 18, 21...

Multiples of 3 can be negative as well:
−3, −6, −9, −12, −15, −18, −21...

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