位值

First off, let's learn some definitions:

Whole numbers are positive numbers that don't have any fractions or decimals. For example, $867$ is a whole number (while $867.5$ or $867\frac{1}{2}$ are not). They can be summarized as the natural numbers plus $0$.

Digits are the symbols that go into numbers: $0, 1 , 2, 3, 4, 5, 6, 7, 8,$ and $9$ are digits. $867$ is not a digit, but it is made up of three of them ($8, 6,$ and $7$).

Place is where a digit is in a number. In $867$, the number $8$ is in the hundreds place, $6$ is in the tens place, and $7$ is in the ones place.

Place value is how much each digit is worth, based on what place it has in a number. You can find a digit's place value by multiplying it times its place. For example, the $8$ in $867$ actually has a place value of $800$ (or $8 \times 100$), since it's in the hundreds place. Similarly, $7$ in $867$ just has a place value of $7$, since it's in the ones place ($7 \times 1$).

If you're familiar with decimals, we can also assign place values to decimals.

$6$ has a place value of $60$ ($6 \times 10$) in $867$, since it's in the tens place.

Basically, if you add up all the place values for a number, you should get the number itself. For $867$, you can do: $$\begin{align} 867&= (8\times100) + (6\times10) + (7\times1)\\ &= 800 + 60 + 7\\ &= \boxed{867} \end{align}$$

(Videos) Place Value

by mathman1024

Here's a video by mathman1024 that explains the place value system for whole numbers.

$\large{\text{Summary}}$

When writing numbers we use a place value system. Each place, or spot, in a number has its own meaning.

Whole numbers are the set of natural numbers (counting numbers) and zero. $$0,1,2,3,...$$

In this video he looks at identifying place values.

The first example is:

The U.S. population which is: $317{,}367{,}038$. What places are the $3$'s in?

Well the rightmost three is in the tens spot. There's three tens or $30$. The middle $3$ is in the hundred thousands spot. The leftmost $3$ is in the hundred millions. Because this is the first number it indicates how large the number is. So the U.S. population is in the hundred millions.

The world population is around $7{,}140{,}490{,}311$. How big is this number?

The first number is in the billions spot so this number is in the billions.

The national debt is $17{,}290{,}698{,}230{,}031$. This is in the trillions.

Lastly he looks at writing numbers out. If you have $23{,}708$ you would write this as twenty-three thousand, seven hundred eight.

Try writing this number out, then watch the video to see the answer.

1. $317{,}367{,}038$

(Video) Place Value

by Math Antics

Here's a video by mathantics that explains place values for numbers and what they represent.

$\large{\text{Summary}}$

Place values of a number range from ones, tens, hundreds, thousands, ten thousands, etc. They keep going. They can also be expressed as $10^0$ ($1$ with $0$ zeros on the end of it), $10^1$ ($1$ with $1$ zero on the end of it), $10^2$ ($1$ with $2$ zeroes on the end of it), etc. A Googol (pronounced like Google) is one of the largest place values we have. It's $10^{100}$ which is a $1$ followed by $100$ zeroes.

It looks a little like this: $$\begin{aligned} 100000000000000000000&\\ 00000000000000000000&\\ 00000000000000000000&\\ 00000000000000000000&\\ 00000000000000000000& \end{aligned}$$

Fun fact: It takes approximately $2$ weeks to count to the number one million. Using this estimate it would take almost a googol years to count to a googol!