# 2.2 Using a Number Line

A number line can help you to visualize many different kinds of numbers.
For example, on the number line below, the intervals between the whole numbers
(or units) have each been split into ten equal intervals: These are tenths. If
each tenth is then split into ten equal intervals, each of the smaller intervals
will be hundredths, since there will be 100 of these intervals in a whole unit. The
number line shows the numbers *two-tenths*, *one unit and three-tenths*, *one unit and thirty-five
hundredths*, and *one unit and eight-tenths*.

To write these numbers in decimal form, the place value table can be
extended by adding columns to the right, as shown below. Since the value of each
column is ten times smaller than the value of the column to its left, the
columns to the right of the units column will represent **tenths**, then
**hundredths**, **thousandths**, and so on.

Let’s look at a specific example. Notice that the value of the digits is based on the number ten, even those to the right of the decimal.

You can see in the illustration above that the following is true:

- 1 is in the
**tens**place. - 7 is in the
**units**place. - 5 is in the
**tenths**place. - 9 is in the
**hundredths**place. - 1 is in the
**thousandths**place.

With decimals, different terminology can also be used to describe a particular placeholder. Often, you will need to round a decimal to a specific position, that is decimal place. Instead of asking you to round to the nearest tenth, you might see instructions to “round to 1 decimal place” (1 d.p.). Below is a table to help you keep track of the math vocabulary.

Tenth | Hundredth | Thousandth | Ten Thousandth |
---|---|---|---|

1 d.p. | 2 d.p. | 3 d.p. | 4 d.p. |

## Activity: Decimal Numbers and Decimal Places

In your math notebook write the place values for each of these numbers.

- (a) 5.603.

### Discussion

Write the numbers in a place value table first starting from the units and working to the right.

- (b) 10.986.

### Answer

(a) 5.603.

- 5 is in the units place.
- 6 is in the tenths place.
- 0 is in the hundreths place.
- 3 is in the thousandths place.

(b) 10.986.

- 1 is in the tens place.
- 0 is the units place.
- 9 is the tenths place.
- 8 is the hundreths place.
- 6 is the thousandths place.

Now identify in parts (a) and (b) which number is in the second decimal place (2 d.p.).

### Discussion

Starting at one count each number to the right of the decimal point this will tell you the decimal place for each number.

### Answer

(a) 5.603.

0 is in the second decimal place.

(b) 10.986.

8 is in the second decimal place.

2.1.5 The Decimal System Compared