KS3 Bitesize

Maths

Whole numbers

Numbers are part of everyday life. It is important that you can write and describe them, and carry out simple calculations without using a calculator.

Introduction

This Revision Bite covers:

Place value

In the number 3 147 286 the figure 2 has a value of 200 (two hundred), and the figure 3 has a value of 3 000 000 (three million).

Question

What is the value of the figure 8 in 3 147 286?

The figure 8 has a value of eight tens, or 80.

Writing and describing

When describing whole numbers, remember the place values of the original digits.

However, some digits are 'joined' in their description. For example - when describing the number 35, we do not say 'three tens and five units', but instead describe it by the more common name of 'thirty five'.

In the same way the thousands, ten-thousands and hundred-thousands columns are usually described together. Here are some examples.

2 000 is described as 'two thousand'
62 000 is described as 'sixty two thousand', and
162 000 is described as 'one hundred and sixty-two thousand'

Example

The number 3 147 286 can be written in words as
three million, one hundred and forty seven thousand, two hundred and eighty six.

Question

Q1. Describe the numbers 4 235 225 in words.

Q2. Write twenty-three thousand and fifty six in figures

A1. Four million, two hundred and thirty five thousand, two hundred and twenty five.

A2. 23 056

Ordering

When you have a series of large numbers that are not in number order, it is sometimes difficult to make sense of them.

Here is a table showing the daily profits of an online music store, written in order of days:

Day Mon Tues Weds Thurs Fri Sat Sun
Profit £5934 £7656 £7573 £8678 £10834 £14976 £5004

If these numbers were put into a place value table, it would be easier to arrange them in order.

Days Tens of thousands Thousands Hundreds Tens Units
Mon   5 9 3 4
Tues   7 6 5 6
Weds   7 5 7 3
Thurs   8 6 7 8
Fri 1 0 8 3 4
Sat 1 4 9 7 6
Sun   5 0 0 4

Look at each column in turn.

The figures for Friday and Saturday will be the largest as these have figures in the tens of thousands column.

Looking at the thousands column shows that there is a 4 in the thousand column for Saturday and a 0 in the thousands column for Friday. Therefore Saturday has the largest number.

Here is the table written in order of days:

Day Sat Fri Thurs Tues Weds Mon Sun
Profit £14976 £10834 £8678 £7656 £7573 £5934 £5004

Multiplying by 10, 100, 1000

Multiply by 10

When we multiply by 10, every figure moves one place to the left. Units become tens, tens become hundreds and hundreds become thousands.

What is 23 x 10?

Multiplying by 10

Move each figure 1 place to the left.

Multiplying by 10

Each figure has moved 1 place to the left. There is a gap in the 'units' column. There aren't any units, so insert a '0'. 23 x 10 = 230.

Multiply by 100

When we multiply by 100, every figure moves two places to the left. Units become hundreds, tens become thousands and hundreds become ten-thousands.

Multiplying by 100

What is 12 x 100?

Multiplying by 100

Move each figure 2 places to the left.

Multiplying by 100

Each figure has moved 2 places to the left. There is a gap in the 'tens' column and the 'units' column. There aren't any tens or units, so insert a '0' in each. 12 x 100 = 1200.

Multiply by 1000

When we multiply by 1000, every figure moves three places to the left. Units become thousands, tens become ten-thousands, and hundreds become hundred-thousands.

Multiplying by 1000

What is 7 x 1000?

Multiplying by 1000

Move each figure 3 places to the left.

Multiplying by 1000

Each figure has moved 3 places to the left. There is a gap in the 'hundreds' column, the 'tens' column, and the 'units' column. There aren't any hundreds, tens or units, so insert a '0' in each. 7 x 1000 = 7000.

Dividing by 10, 100, and 1000

Divide by 10

When we divide by 10, every figure moves one place to the right. Thousands become hundreds, hundreds become tens and tens become units.

Dividing by 10

What is 270 divided by 10?

Dividing by 10

Move each figure 1 place to the right

Dividing by 10

Each figure has moved 1 place to the right. 27.0 is the same as 27, so remove the zero. 270 divided by 10 = 27

Divide by 100

When we divide by 100, every figure moves two places to the right. Thousands become tens, hundreds become units, and tens and units become fractions of a unit.

Dividing by 100

What is 1300 divided by 100?

Dividing by 100

Move each figure 2 places to the right

Dividing by 100

Each figure has moved 2 places to the right. 13.00 is the same as 13, so remove the zeros. 1300 divided by 100 = 13

Divide by 1000

When we divide by 1000, every figure moves three places to the right. Thousands become units. Hundreds, tens and units become fractions of a unit.

Dividing by 1000

What is 4000 divided by 1000?

Dividing by 1000

Move each figure three places to the right.

Dividing by 1000

Each figure has moved three places to the right. 4.000 is the same as 4, so we remove the zeros. 4000 divided by 1000 = 4

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