Introduction: There are some things you should know about place values, but first you should already know about how to draw a number line (Fig. 1), how to putting numbers in ascending and descending order, and how to plot numbers on a scale using whole numbers, fractions, and decimals (see Fig. 2).
For now, we will only deal with whole numbers to review the basics. Later we will look at decimals and fractions.
Part A: Place Value
Let’s first look at place value. Here is an example:
We can think of this number as money. As you can see all numbers are in a particular location. This is called place value, meaning each value has a position and a role to play as a member of this number group, similar to a family.
In English, we read from left to right. So the numbers further to the left are larger numbers. So in order to understand place value, we must work backwards and define each position so that we can read a number correctly. Let’s dissect this number to see what is meant.
Starting from the far right, let’s look at each place value (see Figure 3).
The first position is called the ones place and in our example above that number is 9.
Move one position to the left of 9:
- The second position is called the tens place, and that number value is 5.
Move one position to the left of 5:
- The third position is called the hundreds place, and that number is 4.
And we continue. Take a moment to locate each place value for our example number above. Be sure to commit the place values to memory. When we get into higher math this will be an important foundational step.
<PLACE VALUE QUIZ>
We could continue naming place value positions because numbers don’t end. They continue for infinity, or forever. Some examples of numbers that go beyond trillion include, quadrillion, quintillion, and dectrillion.
The point is, each position has a specific name. The reason why knowing place value is important is because the place values tell you how much we have. Knowing your place value for numbers is fundamental working addition problems. Another importance to place values is that they teach us how to read values and write numbers in word form.
Now let’s look at a few examples:
How would you say this value?
You’d say “one trillion, eight hundred seventy-four billion, three hundred four million, thirty-nine thousand, two hundred seventy.”
Notice that when writing numbers we only hyphenate numbers between twenty and ninety-nine. Also, notice that there is no “and” in this statement. Using the word “and” means we have two parts – which is incorrect. This is only one value. This is a big number, but it is a whole number. You’d use the word and to denote bringing two whole numbers together or a part of another number, like in decimals. We will discuss more of this in a later lesson.
- What place value is the 3 in the number 93,205?
- What place value is the 7 in the number 679,430,125?
<Examples or Quiz Here>
In Lesson 1 Part B we will learn about expanded form, how this relates to addition, and why it is important.