Once children are fluent in their understanding of units, tens, hundreds and thousands, they should begin to explore how the number system continues to develop with larger numbers. Place value headings beyond thousands are as follows:

Ten Millions

Millions

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Units

TM

M

HTh

TTh

Th

H

T

U

Most countries use a thin space to separate groups of thousands, and a ‘point’ as a decimal mark. In the US, commas are used to separate groups of thousands. (You will sometimes see this used in the UK in older materials.) Some countries use a comma as a decimal mark

Using this understanding, children should develop fluency in reading numbers such as 12 345 678. They should also be able to write numbers in figures when they are given in words, for example, six million, four hundred and two thousand and seventy six.

Children also need to be able to recognise the value of a digit in these large numbers and apply this understanding to arrange numbers in order of size.

What this might look like in the classroom

Question 1

Write in words the number 13 450 031

Answer 1

Thirteen million, four hundred and fifty thousand and thirty one

Question 2

What is the value of the red digit in the following number? Write your answer in words.
9 439 702

Answer 2

Thirty thousand

Question 3

Write these numbers in order of size, starting with the smallest.

The decimal number system continues further of course. The next few place value headings are:

Hundred Billions

Ten Billions

Billions

Hundred Millions

Ten Millions

Millions

Hundred Thousands

Ten Thousands

TM

M

HTh

TTh

Many children are fascinated by finding ever-larger numbers. Named by a nine-year old, a googol is a ‘one’ followed by one hundred zeroes. This number (10^{100}) is far greater than the number of atoms in the universe (no more than 10^{80}). A googolplex is a ‘one’ followed by a googol zeroes which is impossible to write down. Google is named after a googol, and their headquarters is known as the Googleplex.

The fact that a number can always be made bigger by adding another number to it results in the concept of infinity. Infinity is not a number, but a way of describing the concept that there is no limit to the number of numbers.

In the UK it was once the case that a billion was 1 000 000 000 000, while in the US 1 000 000 000 was a billion. In 1974 the UK adopted the US definition of one billion although many European countries still do not. Connected to this, there are still two ways of defining a trillion.

Making connections

Children will need to use their understanding of large numbers to solve problems involving rounding to the nearest one hundred thousand or to the nearest million.

In the future, pupils will begin to appreciate how the decimal number system is so named because it is based on powers of 10.

Ten Millions

Millions

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Units

TM

M

HTh

TTh

Th

H

T

U

10×10×10×10×10×10×10

10×10×10×10×10×10

10×10×10×10×10

10×10×10×10

10×10×10

10×10

10

10×110 or 10÷10

10^{7}

10^{6}

10^{5}

10^{4}

10^{3}

10^{2}

10^{1}

10^{0}

Using a different number as the base results in a different number system. For example, binary is ‘base-2’

128

64

32

16

8

4

2

1

2×2×2×2×2×2×2

2×2×2×2×2×2

2×2×2×2×2

2×2×2×2

2×2×2

2×2

2

2×12 or 2÷2

2^{7}

2^{6}

2^{5}

2^{4}

2^{3}

2^{2}

2^{1}

2^{0}

The number ‘twelve’ is 12 in base-10 and 1100 in binary