Things That Make Place Value Easy
1. There are only 26 letters in the English alphabet. That's all. Ain't no more. Yet, we use these 26
letters over and over again to make words. There are just over 171,000 words we use and another
46,000 words we no longer use. In order to spell a word correctly, we have been taught that the letters
go in a certain order, so that to spell "goof" correctly, we can't spell it foog - even though the letters are
the same.
2. There are only ten digits (0,1,2,3,4,5,6,7,8,9). We use these digits over and over again. We don't
spell numbers when we write them out in expanded or customary form - we use 'place value.'
3. The key to place value is the decimal. The decimal - and nothing else - determines the value of a
number. We use digits to make numbers in the same fashion we use letters to make words. And we
use certain rules to make sure we do so correctly.
4. Remember this forever: All numbers - every single one - has a decimal. Just one decimal per
number. And, the decimal can be moved (left or right) in order to solve a math problem. But, if the
decimal moves, the value of the number changes because the decimal was moved. The digits stay in
the same order.
5. Here's how the decimal works: the decimal anchors the position of the one's place. Every other
place value is determined by its relationship to the one's place - which is determined by the decimal.
Every place value to the left of the decimal is a whole number; every place to the right of the decimal is
part of a whole - like a fraction. You write the number 528.43 like this:
5
2
hundred's
ten's
8
.
4
3
one's . tenth's hundredth's
When you move the decimal, the digits stay in the order - 5, 2, 8, 4, 3 BUT the value of the digits
change. For example, if you move the decimal one place to the left, the new number is: 52.843
5
ten's
2
.
8
4
3
one's . tenth's hundredth's thousandth's
When you move the decimal, the digits stay in the order - 5, 2, 8, 4, 3 BUT the value of the digits
change. For example, if you move the decimal one place to the right, the new number is: 5,284.3
5
2
8
4
one thousand's hundred's ten's one's
.
.
3
tenth's
6. Things to remember about the goofy decimal: when you move the decimal just one place - either
left or right - it changes the value of the original number ten times. If you move two places, it changes
the value of the original number 100 times because each place value position has a value ten times
smaller or larger (depends on which way you look - left or right) of the place value next to it. Example:
Original number: 234.00. Move the decimal two places to the left; the new number is 2.34 - a
hundred times smaller than 234.00. If you move the decimal two places to the right, the new number
is 23,400.00 - a hundred times bigger.
Even more exciting stuff on page two! Honest!
7. So, you may thinking about 235 as a number. Don't see a decimal? It's there - to the right of the
five. The rule in math is: if there is no value to the right of the decimal - you don't have to "turn the
decimal on." Or show it to the right of the one's place. The best example of this is money:
You can write 45 dollars as $45.00 or $45 because there is no value after the one's place (the five).
But if you have a price higher than an even $45 but lower than an even $46 dollars - you have to show
the decimal place: $45.78. If you don't show the decimal, then the price would be $4,578. See the
difference? The decimal makes sure you wanted the five in the one's place. Remember, move the
decimal, change the value of the number. I might be willing to buy a new tire for $45.78 but not $4,578!
So, remember, the number 7. is not a digit. Numbers have place value, digits do not.
8. Rounding numbers. You always round a number to a place value. There is no other way to round a
number. That's why 3 rounded to the ones stay 3. That's why 473 rounded to the one thousands
place becomes a zero. You don't always change a number when you are rounding - check it first before
you change the number.
9. What about other goofy stuff? In the number 235, there are still place value positions greater (to
the left) than the hundreds place - in this case all the values are empty - zero - so you don't have to
show the zeros. Just like to the left of the five, there are smaller place values to the right but they are
empty as well - so you don't have to put the decimal or the zeros.
10. What about this number: 2,034? You need to show the zero to maintain proper place value
because you have two thousand but no hundreds. And since you have no values greater than the one
thousands place or smaller than the ones place, you don't have to write it like this 2,034.00 or
002,034.00. Which is the same number, only it looks funny because you wrote in zeros you don't need.
11. The decimal place organizes numbers so we can add, subtract, multiply, and divide. When you add
362 to 23 you add place value to place value so that it is written like this:
.
.
.
362
23
385
and not like this:
362
23
592
Remember: You always start from the lowest place
value and work to the left when you
add, subtract, or multiply. but not
when you divide.
12. Think about 725.00; in expanded form you would write it as:
700 + 20 + 5. + .0 +
.00
The single zero means that you have 2 groups of ten; the double zero means you have 7 groups of
hundreds. The zeros behind the decimal place (or to the right of the decimal place) mean you have no
value in those places. But writing numbers like this would take forever - like math class. So the
folks who made the rules decided that it would be OK to drop the zeros you don't need and just write:
725.00
Told you this was excitin'!
or
725