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Place Value (and the decimal system)

In the past, there were many different methods of representing numbers (e.g. Roman numerals).

Today, most of the world uses a place value system based on powers of 10.

For example: 5280 => 5 thousands, 2 hundreds, 8 tens, and 0 units

Another way of writing it would be:

5280 = 5×1000 + 2×100 + 8×10 + 0×1

When we read whole numbers like the own above, we understand that the 5 actually represents

five thousand, the 2 represents two hundred, and so on, because of these numbers’ positions

relative to an imaginary reference point on the right side of the “units” digit.

When we want to represent fractions using the same type of positional notation, we use a

decimal point. In North America and the United Kingdom, the decimal point is represented by a

period (.), while in continental Europe, and some other parts of the world, it is represented by a

comma (,). The decimal point separates the numbers that represent whole amounts from the ones

that represent fractional amounts.

For example: 32.174 => 3 tens, 1 unit, 1 tenth, 7 hundredths, and 4 thousandths.

Another way of writing it would be:

32.174 = ( 3 × 10 ) + ( 2 × 1 ) + �1 ×

� + �7 ×

� + �4 ×

�

100

1000

You can see from this that the three digits to the right of the decimal all represent fractions (that is,

quantities smaller than one).

Rounding

Sometimes when you are working with decimal numbers, there are too many digits in your answer

and you need to make the answer shorter by rounding it off. Before rounding, you need to decide

how many decimal places (digits to the right of the decimal) you want to keep.

For example, 32.174, rounded to two decimal places, would be 32.17. You can see that the result

only has two digits to the right of the decimal. In this case, I am rounding down, because the result

after rounding is a lower number than we had before.

The number 153.378, rounded to two decimal places, would be 153.38. In this case, we are

rounding up, because the result after rounding is a higher number than we had before.

“Rounding to two decimal places” is another way of saying “rounding to the nearest hundredth”.

Can you see why? This is because the place to the right of the decimal is the hundredths place. In

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This document last updated: 7/27/2011

Student Academic Learning Services