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 a 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.

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.