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# Lesson 3: Place Value to 100

*Place value is a confusing concept for many students, and many
students don't fully understand what it means for a digit to be in a
particular place. This lesson introduces this important topic.*

**Don't forget to watch the embedded YouTube
video clip for this lesson at the bottom of the
page. **

We use what is called a base-10 math system. What that means is that we use the digits 0 to 9 to represent quantities from zero to nine. Once we get to ten, we need to use two digits to represent numbers, since we only have symbols for 0 to 9.

To represent the quantity ten, we write "10". What this actually means is that we have one 10, and zero 1s. We can say that the "1" is in the "tens" place, and the "0" is in the "ones" place. This is how our world represents numbers, and this system was probably established because we have 10 fingers.

Take a look at the number 37. Make sure you understand that this is actually three 10s (which is 30), and seven 1s (which is 7), forming the number thirty-seven (30+7). We add the values of each place (each column) to determine the number that is represented.

Some students think that it doesn't matter if you write 37 or 73, since they both use the same two digits. Make sure you understand that the rightmost column tells you the number of 1s you have, and the column to the left of that tells you have many 10s you have. To determine the number of represented, add the number of 10s to the number of 1s. For example, above we have thirty-seven followed by seventy-three.

Once we get passed 99 (ninety-nine), we need to add yet another column to represent numbers. To the left of the 10s place, we have the 100s place. If we write "100", it means one 100, plus zero 10s, plus zero 1s.

Take a look at the number 748. This means seven 100s (making 700), plus four 10s (making 40), plus eight 1s (making 8), for a total of 748 (seven hundred forty-eight).

Remember, to determine the value of a number, just look at the place
value of each digit. **Memorize** this chart, and
make sure you fully understand how this topic works.

Hundreds | Tens | Ones |

3 | 4 | 5 |

300 | 40 | 5 |

Using the chart above, we can see that 345 (three hundred forty-five) really means 300+40+5.

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