Maths Difficulties and Dyscalculia. A series of blogs by Steve Chinn

www.mathsexplained.co.uk     

2. Big numbers: A billion.

My younger daughter has special needs. When I was visiting her special school, the teacher showing me around said to a class, ‘This is Dr Chinn. He is a famous (?) maths specialist. Do you want to ask him a question?’ ‘Yes’ said one thirteen year old, ‘What’s a billion?’

That’s a tough question to answer quickly. So, here is a longer answer.

It’s all about thousands.

One thousand is 1,000. It’s a 4-digit number and has three zeros.

One million is a thousand thousands, 1,000 000. It’s a 7-digit number. 

One billion is a thousand millions, 1,000 000 000. It’s a number with 10 digits

So how can we create a picture that shows us just how big these numbers are?

I’m going to use volume to create visual images that should help you to compare these numbers. So, can you picture a cube? It’s a 3-dimensional shape where all the sides are the same length. It’s a 3D version of a square

Start with a cube for one. This is going to be a little cube with all its sides 1cm (1 centimetre) long. It will have a volume of 1 cubic centimetre. This is our start, a one cube.

So, this cube is 1 cm high, 1 cm wide and 1 cm deep.

My next cube is a box that will hold a thousand, 1000 of the one cubes. The three dimensions are each 10 cm. This creates a volume of 10 x 10 x 10, that is a one thousand cube, 1000. It will hold 1000 of the one cubes. 

This 1,000 cube is 10 cm high, 10 cm wide and 10cm deep.

By the way, if you had that much water it would weigh 1 kilogram.

Now, for a million, we need 1000 of these one thousand cubes, that will build into a cube where all the sides are 1 metre (100 cm) long. That makes 100 x 100 x 100 which is 1,000,000. This one metre cube will hold one million of the one cubes.

This cube is 100 cm (1m) high, 100 cm (1m) wide and 100 cm (1m) deep.

By the way, if you had that much water it would weigh 1 tonne.

I hope you are seeing a pattern here. The billion cube is going to be made up of 1000 of the 1 metre x 1 metre x 1 metre cubes. Since each metre cube can hold 1000 of the one cubes, then the new cube will hold 1000 lots of a million of the one cubes 1,000 000 000

Each side of the billion cube is 10 metres (1000 cm) long. (To give you some idea of size, 10m is about half the length of a ten-pin bowling lane).

Our billion cube has a volume of 1000 x 1000 x 1000 one cubes. A thousand times a thousand times a thousand is a billion. A thousand lots of a thousand is a million. A thousand lots of a million is a billion.

If the next name in this sequence is a trillion, can you work out how to write a trillion in digits? How many zeros in your trillion?