# 2 Scientific notation and large numbers

So how can you use powers of ten to write numbers in scientific notation? Let’s look at the example of six million to start with. Written in full this number is six followed by six zeroes: 6 000 000. This can also be written as: . Now 6 million is shown like this it can be written using a power of ten by noting that:

10 multiplied by itself 6 times is the same as 10^{6}

So,

So, this now means that 6 million can be written as:

You would therefore write 6 million using scientific notation as: .

Similarly, if the example had been six and a half million (6 500 000), this can be written in scientific notation as:

or in scientific notation.

So, a number written in scientific notation takes the form of: a number between **1 and 10** multiplied by a whole number power of 10. This can be shown mathematically as:

Thus, there are two steps to writing a number using scientific notation, as follows:

- Work out what the number between 1 and 10 will be.
- From this, decide on the power of 10 required.

So, taking the example of 130 000, the number between 1 and 10 must be 1.3, as it cannot be 0.13 or 13. 0.13 is less than 1, and 13 is greater than 1.

So, 130 000 written in scientific notation is . Now, it’s your turn to try some examples.

## Activity 2 Understanding and writing numbers in scientific notation

Write the following numbers without using powers of 10.

- a.

### Answer

- a.

- b.

### Answer

- b.

- c.

### Answer

- c.

Write the following numbers in scientific notation.

- d.92 billion

### Comment

1 billion is 1 followed by 9 zeroes.

### Answer

- d.

- e.400 trillion

### Comment

1 trillion is a million million.

### Answer

- e.

- f.9 500 000 000 000

### Answer

- f.

- g.Which of these numbers is the biggest?

### Comment

Compare the powers of ten.

### Answer

- g.The highest power of the three numbers in this activity is 14, so 400 trillion is the biggest number here.

Now you’ve found out how to write large numbers using scientific notation, in the next section you’ll turn your attention back to the problem posed at the beginning of this week: how to work out the width of the observable universe in kilometres.