# Decimal numbers

## Decimal calculations

Decimal numbers relate to the numbering system we use ― counting by tens. But they also refer to any number that includes a decimal point (a decimal fraction).

Decimals are a common way to express fractions in the building industry.

Look at the following information about decimal calculations.

## Decimal fractions

For fractions often, instead of writing one number above another, a decimal point is used. For example:

3/10 (three tenths) written as a decimal is 0.3 (zero point three).

9/10 (nine tenths) written as a decimal is 0.9 (zero point nine).

Most of the fractions that you deal with will be decimal fractions. The metric system uses decimals.

## Decimal numbers

Decimal fractions relate to tenths, hundredths, thousandths, etc. The image below shows the makeup of a decimal number. The number shown to the left of the decimal point (25) is a whole number (two tens and five units).

The number to the right of the decimal point (386) is a decimal fraction (three tenths, eight hundredths and six thousandths).

## Fractions as decimals

Fractions can be shown as a decimal fraction. Examples:

1/2 is the same as 5/10 as a decimal fraction is 0.5

1/4 is the same as 25/100 as a decimal fraction is 0.25

3/4 is the same as 75/100 as a decimal fraction is 0.75

1/3 is almost the same as 33/100 as a decimal fraction is 0.33

## Working with decimals

When doing calculations with decimals, for example adding, list the numbers with the decimal points aligned. An example is shown below:

1,075.000
248.320
5,789.654
456.100
56.990
Total 7,626.064

Notice extra zeros are added to give each number tenths, hundredths and thousandths. ## Exercise 1

The materials for this job have come from four different suppliers.

The list below shows the costs from each supplier:

\$1,524.60
\$8,900.55
\$648.23
\$12,536.10.

What is the total cost of the materials? ## Exercise 2

The area of the bedrooms on this house plan are:

• bedroom 1 = 13.4 m²
• bedroom 2 = 6.33 m²
• bedroom 3 = 5.25 m².

What is the total area of the three bedrooms?

Submit ## Exercise 3

The cost of materials, including tax, for a building job is \$1,576.89. The included tax is \$157.69.

What is the cost of materials before tax? ## Exercise 4

You need to cut a 2.845 metre piece of timber from a 3.3 metre length of timber. Calculate the length of the left over piece of timber.

Submit ## Exercise 5

To attach the plasterboard to the walls and ceiling of a house, you need 896 screws. Each screw costs \$0.13 (13 cents).

What is the total cost of the screws? ## Exercise 6

It costs \$18.75 per square metre to paint the inside walls of a house.

If the inside wall area of the house is 137.4 square metres, how much will it cost to paint the walls? ## Exercise 7

The plans for a new building show a room that has a length of 6.75 metres. The spacing between each ceiling joist for the room is to be 0.45 metres.

You need to calculate how many spaces there will be.

Submit ## Exercise 8

467.5 linear metres of framing timber has been used for a job. The total cost of the timber used is \$1608.20.

You need to calculate the cost of the timber per linear metre.

## Rounding

Decimal calculations often have answers with a lot of decimal places, like these:

7196.807556
3.1415926535897932384626433832795
14.87999

Rounding is reducing the number of digits. In most cases one, two or three decimal place is accurate enough.

### How to round

• Decide which is the last digit to keep (how many decimal places).
• Don't change the last digit if the next digit is less than five.
• Increase the last digit by one if the next digit is five or more.

Example 1

4528.85499 rounded to 2 decimal places is 4528.85

Example 2

103.807556 rounded to 3 decimal places is 103.808

## Rounding examples

The table below shows three numbers rounded.

7196.807556
3.1415926535897932384626433832795
14.87999

Rounding examples
three decimal places two decimal places one decimal place no decimal places
7196.808 7196.81 7196.8 7197
3.142 3.14 3.1 3
14.880 14.88 14.9 15 ## Exercise 9

Given the number 45.675348 which of the following most accurately shows it rounded to three decimal places? ## Exercise 10

Given the number 6.6758 which of the following most accurately shows it rounded to one decimal place? ## Exercise 11

Round this number to two decimal places.

12.4156321

Submit ## Exercise 12

Round this number to one decimal place.

99.99999

Submit ## Exercise 13

Round this number to three decimal places.

159.9994156321

Submit

## Summary

This is the end of the section on calculations with decimal numbers.

Key points to remember are:

• decimal fractions are tenths, hundredths, thousandths, etc of a whole thing
• decimal fractions are written with a decimal point
• rounding is reducing the number of decimal places displayed.

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