# What Is Place Value?

There are an infinite number of numbers. Imagine having to invent a new symbol for every number out there. It would be impossible to invent or remember.

To get around this problem, we have invented a decimal number system, which uses 10 digits.

But does that mean we can only have 10 numbers? No. By putting the digits in a different position, or place, within a number we can write an infinite number of number.

For example, a digit 1 here...

makes the number one. But a digit one placed here...

makes ten.

This is place value. The same digit has different values depending on its place in a number.

# What Are the Different Place Values?

The place values are called hundreds, tens, units etc.

Consider the number 248.35:

• The 2 is in the hundreds column. It has a value of 200.

• The 4 is in the tens column. It has a value of 40.

• The 8 is in the units column. It has a value of 8.

• The 3 is in the tenths column. It has a value of 3/10ths.

• The 5 is in the hundredths column. It has a value of 5/100ths.
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# COMPARING THE VALUE OF PLACE VALUES

If you go left along a number, each place value is ten times bigger than the one to its right.

If you go right along a number, each place value is ten times smaller than the one to its left.

WHY DO WE HAVE 10 DIGITS?

The decimal number system uses the digits

0 1 2 3 4 5 6 7 8 9

And each place value is 10 times bigger than the one to its right.

This is most probably because we have 10 digits (fingers and thumbs), so counting in tens seems natural to use.

# OTHER NUMBER SYSTEMS

Computers use a binary number system, that uses two digits

0 1

Each place value is twice the size of that to its right.

The is also an octal number system with 8 digits

0 1 2 3 4 5 6 7

Each place value is 8 times bigger than the one to its right.