What is the difference between face value and place value of digits?
Before we proceed to face value and place value let us recall the expanded form of a number.
The expanded form of 534 is 500 + 30 + 4
We read it as five hundred thirty four.
Similarly, 798 = 700 + 90 + 8
We read it as seven hundred ninety eight.
2936 = 2000 + 900 + 30 + 6 = Two thousand nine hundred thirty six
For example similarly, all numbers can be written in expanded form and read accordingly.
(i) 35 = 30 + 5 = Thirty five
(ii) 327 = 300 + 20 + 7 = Three hundred twenty seven
(iii) 942 = 900 + 40 + 2 = Nine hundred forty two
(iv) 1246 = 1000 + 200 + 40 + 6 = One thousand two hundred forty six
(v) 3584 = 3000 + 500 + 80 + 4 = Three thousand five hundred eighty four
(vi) 5167 = 5000 + 100 + 60 + 7 = Five thousand one hundred sixty seven
The digits of a number express the values of their own when the number is given in expanded form and read in words. The value of a digit when expressed in expanded form of the number is called its place value in the number.
(i) In the number 378;
the place value of 3 is 300 (three hundred)
the place value of 7 is 70 (seventy)
the place value of 8 is 8 (eight)
(ii) In the number 5269;
the place value of 5 is 5000 (five thousand)
the place value of 2 is 200 (two hundred)
the place value of 6 is 60 (sixty)
the place value of 9 is 9 (nine)
Thus, the place value of a digit in a number is the value it holds to be at the place in the number. If 5 is at Thousand-place in a number, its place value will be 5000, if it is at Hundred-place, its value will be 500, etc.
In the number 2137, 2 is at Thousand-place, 1 is at Hundred-place, 3 is at ten’s-place and 7 is at one’s-place. So, the place values of the digits 2, 1, 3 and 7 are 2000, 100, 30 and 7.
The face value of a digit is the digit itself, at whatever place it may be. It is unchangeable and definite. But place value changes according to the digit’s place.
For example; to find face value and place value of 3572:
face value of 2 is 2 place value of 2 is 2
face value of 7 is 7 place value of 7 is 70
face value of 5 is 5 place value of 5 is 500
face value of 3 is 3 place value of 3 is 3000
The face value as well as place value of zero (0) is always (0).
We used the spike-abacus to show, to read and to write a number properly. Now with our knowledge of the values of the digits we read and write the numbers without the help of an abacus.
This abacus shows the number 423.
According to the abacus,
4 beads are at H-place (hundred-place)
2 beads are at T-place (ten’s place)
3 beads are at one’s place
Hence, the number = 400 + 20 + 3 = 423
Now, having the knowledge of face value and place value of the digit, we ascertain the total value of a number; as:
the face value of 4 is 4 and place value of 4 is 400
the face value of 2 is 2 and place value of 2 is 20
the face value of 3 is 3 and place value of 3 is 3
So, 423 = 400 + 20 + 3
It is read as, four hundred, twenty and three or four hundred twenty three.`