Place value

Digits 0,1,2,3,4,5,6,7,8, and 9 can be used to write numbers.

Examples of WHOLE numbers are made up of digits, and are as follows: 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14, . . .

There is another type of number which is made up of WHOLE numbers.  These numbers are called NATURAL numbers.

------- The smallest digit is "0".
------- The largest digit is (there is no largest digit) because the series of dots ". . . " means that the list
-------- goes on and on forever without ending.

++++ The smallest NATURAL number is "1" while the smallest WHOLE number is "0".
++++ The largest NATURAL number is (there is no largest) remember the ". . ." thing?

Figure A

zzThe significance of the (figure A) is that whole numbers are used in mathematical operations.

A whole number is made up of digits (see list above).

====== Mathematical operations are things that we DO to numbers like addition, subtraction,
====== multiplication and so on.  These operations always follow established rules so that
====== when you add 1 + 1 and get 2, this is the same answer that everyone else will get when
====== they add 1 + 1.

PLACE VALUE

LINK TO INTERACTIVE LESSON

In the image to the right you will notice the distance between Mercury and Earth is given using the following digits:  48,337,000

These digits are all whole numbers.  You will notice however that there are two "3s" in this value.  Even though the number "3" is repeated, they DO NOT represent the SAME value.

The reason for this is because that each one of the "3s" are placed in a different POSITION  .

The PLACE value of the 3 on the left is HUNDRED THOUSANDS while the value of the 3 on the right is TEN-THOUSANDS.

Notice how THE PLACE of each digit is what actually determines its VALUE.  This is why we have the term PLACE VALUE.

The digit whether it is 0 or 9 is the first step in determining the value - however the final step in determining the VALUE is where you put the digit.

####### Think of it like this; if there is a dollar bill on the table it is worth a dollar, but it has little
####### value to YOU because it is on the table.

####### If the dollar is in YOUR hand it has a certain value to YOU, if it is in your neighbors hand
####### the dollar is still worth 100 pennies, but it now has little VALUE to you.

####### In this simple example, nothing about the dollar bill changed except its LOCATION.
####### Likewise a digit can stay the same and only change LOCATION in the PLACE VALUE
####### chart meaning that its value is dependent upon its LOCATION just like the value of money
####### is dependent upon whether it is in your hands or your neighbors hand.

Sample problem:

Find the PLACE VALUE of the digit 7 in each whole number listed below:
*****1) 37,860,004   ------- millions place
*****2) 68,790   -------- hundreds place
*****3) 478,936  --------- ten-thousands place

Consider the following number:  Say this number out loud.  When you do, notice how you pronounce the PLACE value of each digit.

3,256 ----- three THOUSAND, two HUNDRED and FIFTY SIX.

------- the three is in the thousands place, the two is in the hundreds place, the five is in the tens place and the six is in the ones place.

Sample problems:

1)  For the number 2768, what does the 2 mean?

A    2 Units                    

B    2 Tens

C    2 Hundreds

D    2 Thousands

Then the 2 means 2 Thousands







2) For the number 9053, what does the 0 mean?

A   0 Units

B   0 Tens

C   0 Hundreds

D   0 Thousands

                                                      Therefore the 0 means 0 Hundreds.