# 10.1.2 Scientific Notation

A number written in scientific notation has the following form:

Notice that to write a number in scientific notation, you can start by writing down the number between 1 and up to but not including 10. So for 130,000, this number is 1.3; then multiply this number by 10 repeatedly until you reach the number required.

Each time you multiply by 10, the power of 10 increases by 1. So, because you have to multiply 1.3 by 10 five times to get 130,000.

## Activity: Understanding Numbers in Scientific Notation

Write the following numbers without using powers of 10.

(a)

### Answer

(A)

(b)

### Answer

(b)

(c)

### Answer

(c)

## Activity: Writing Numbers in Scientific Notation

Write the following numbers in scientific notation.

(a) 92 billion

### Answer

(d)

(b) 400 trillion

### Comment

1 trillion is a million million.

### Answer

(b)

(c) 9,500,000,000,000

### Answer

(c)

Which of these numbers is the biggest?

### Comment

Compare the powers of ten.

### Answer

Notice how using scientific notation enables you to compare the sizes of numbers quickly. The highest power of the three numbers in this activity is 14, so 400 trillion is the biggest number here.

Relating to very small and very large numbers and what they mean is difficult. You may find that this website [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] which allows you to zoom out from the extremely small scale to the very large scale will start to help with this.

10.1.1 Powers of 10