Number Systems & Place Value

In the United States, and many places in the World, a decimal place value system with Hindu-Arabic numerals is used. However, this is not the only form of writing numbers nor is it the only one used in very field. Some fields use other systems, and I will go over a few of the older ones and some others that are currently used. However, to start it is best to start with what we know, the decimal place value system with Hindu-Arabic numbers.

Hindu-Arabic Numbers & Decimal Place Value

We use the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. These are based on older forms from Hindu and Arabic systems. Prior to these, the ‘Western World’ predominantly used Roman Numerals, to be discussed separately.

With these ten digits, we also use a decimal place value. It is called a decimal place value as it is based on ten, decimal coming from Latin, deci for tenth.

Decimal Place Values
3 2 1 0 -1 -2 -3
words thousands hundreds tens ones tenths hundredths thousandths
numbers 1000 100 10 1 0.1 0.01 0.001
Powers of 10 103 102 101 100 10-1 10-2 10-3


For example if we have 3,678 we could also write out the number in words to be:
three thousand 6 hundred seventy-eight. In the US and many other countries we use a dot ‘.’ for the decimal and a comma ‘,’ to mark every 3 digits to the left of the decimal for easier reading. Some other countries switch these, be careful which you need to use. If we are on the right side of the decimal place we sometimes leave a space every 3 digits for easier reading, for example 0.346 680 876. The 0 in front of the decimal place is a good idea to help the decimal stand out, but it is often left out when doing scratch work.

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