Place Value of Whole Numbers

So, what is place value of a whole number?

In a whole number value of digit depends on its place (position) in the number.

The rightmost digit is ones, next to the left tens, next hundreds, then thousands, ten thousands, hundred thousands, millions, ten millions; etc.

Example 1. Determine place value of each digit in 3156.

`\underbrace 3_(text(thousands))\quad\underbrace 1_(text(hundreds))\quad\underbrace 5_(text(tens))\quad\underbrace 6_(text(ones))`.

Next example involves more digits.

Example 2. Determine place value of each digit in 58365738746.

`\underbrace 5_(text(ten billions))\quad\underbrace 8_(text(billions))\quad\underbrace 3_(text(hundred millions))\quad\underbrace 6_(text(ten millions))\quad\underbrace 5_(text(millions))\quad\underbrace 7_(text(hundred thousands))\quad\underbrace 3_(text(ten thousands))\quad\underbrace 8_(text(thousands))\quad\underbrace 7_(text(hundreds))\quad\underbrace 4_(text(tens))\quad\underbrace 6_(text(ones))`.

In last example we saw pretty long number 58365738746.

It is better to write them in standard notation, seprating digits into groups of three starting from right, like 58,365,738,746.

Example 3. Write 46736 in standard notation.

Answer: 46,736.

Finally note, that, for example, in number 524 there is no thousands.

But we can easily add it! 524 is same as 0524. This means that thousand is 0.

We can add as many leading zeros (and ignore them) as we want to the whole number.

For example, 524 is same as 0524 or 0000524.

Warning! But we can ignore only leading zeros: 504 IS NOT the same as 54, although 00504 is same as 504.

Now, it is your turn. Take a pen and paper and solve following problems:

Exercise 1. Determine place value of each digit in 56892.

`\underbrace 5_(text(ten thousands))\quad\underbrace 6_(text(thousands))\quad\underbrace 8_(text(hundreds))\quad\underbrace 9_(text(tens))\quad\underbrace 2_(text(ones))`.

Now, slightly harder exercise.

Exercise 2. Determine place value of each digit in 87587874.

`\underbrace 8_(text(ten millions))\quad\underbrace 7_(text(millions))\quad\underbrace 5_(text(hundred thousands))\quad\underbrace 8_(text(ten thousands))\quad\underbrace 7_(text(thousands))\quad\underbrace 8_(text(hundreds))\quad\underbrace 7_(text(tens))\quad\underbrace 4_(text(ones))`.

Finally, exercise on standard notation.

Exercise 3. Write 3446736 in standard notation.

Answer: 3,446,736.