# 10.1.6 Small numbers and Scientific Notation

In the preceding section you have seen how to write numbers that are less than 1 using powers of ten. So you can now write numbers less than 1 in scientific notation. For example,

An alternative way to write a number less than 1 in scientific notation is first to write it down as a number between 1 and up to but not including 10; in this case it is 3. Then divide this number by 10 repeatedly until you reach the number required. Each time you divide by 10, the power of 10 reduces by 1. So here you have to divide 3 by 10 twice to get 0.03, so .

To convert a number in scientific notation back into decimal form, write down the negative power of 10 as a fraction and then divide the numerator by the denominator. For example:

## Activity: Understanding Small Numbers in Scientific Notation

Write down the following numbers as decimals.

(a)

### Answer

(a)

(b)

### Answer

(b)

(c)

### Answer

(c)

## Activity: Writing Small Numbers in Scientific Notation

Write down the following numbers in scientific notation.

(a) 0.000007

### Answer

(a)

(b) 0.0742

### Answer

(b)

(c) 0.0000000098

### Answer

(c)

Before we move on, think about how scientific notation fits in with what you already know about decimals. Earlier, you saw that when you multiplied a number by 10, the decimal point in the number moved one place to the right, and when you divided a number by 10, the decimal point moved one place to the left. So, extending this idea, if you multiply a number by , the decimal place will move three places to the right to make the number bigger. For example, . Similarly, if you multiply a number by , which is the same as dividing by , the decimal point will move four places to the left to make the number smaller. For example, .

If you want some more practice with scientific notation before you move on to look at how to use scientific notation on a calculator, have a go at this game [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .

10.1.5 Negative Exponents