Place Value: Whole Numbers

So, for instance, the expression "264" means "two 100s, plus six 10s, plus four 1s", because hundreds, tens, and ones are what are stored in those particular places. In what is called "expanded notation", the number "264" can be written as:

Our place-value system is called the "decimal" system, because it's based on "all my fingers" (in other words, on the fact that we have ten fingers). That is to say, the "base" of our number system is ten. We start with ones, being our fingers (that is, being our counting "units"). Then we go to tens, being sets of fingers. Then we go to ten sets of ten fingers, which is 10 × 10 = 100; that is, we go to hundreds.

In other words, every time we go one "place" further to the left (that is, every time we go into a unit that is one jump bigger than the previous place's unit), we multiply by our base of ten:

The commas marking off sets of three digits, like the comma between the 1 to the left and the three 0s to the right in "1,000", are used to make it easier for people to read the numbers. Properly, if you spell out a number in words, you should use commas at those same spots. So 1,234 would be spelled out as "one thousand, two hundred thirty-four".

• Write the number 32,067 in expanded notation.

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• Write the standard form for the number which, in expanded notation, is written as follows: 9,000 + 300 + 2

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• For the number 52,973, (a) state the place held by the 2, and (b) state the digit in the tens place.

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• State the number 622,937,285 in words.