What is the difference between the face value and the place value of the digits?
Before moving on to face value and place value, let’s remember the expanded form of a number.
The expanded form of 534 is 500 + 30 + 4
We read it as five hundred thirtyfour.
Similarly, 798 = 700 + 90 + 8
We read it as seven hundred ninetyeight.
2936 = 2000 + 900 + 30 + 6 = two thousand nine hundred thirtysix
In a similar way, for example, all numbers can be written in expanded form and read accordingly.
(i) 35 = 30 + 5 = thirtyfive
(ii) 327 = 300 + 20 + 7 = three hundred twentyseven
(iii) 942 = 900 + 40 + 2 = nine hundred fortytwo
(iv) 1246 = 1000 + 200 + 40 + 6 = one thousand two hundred fortysix
(v) 3584 = 3000 + 500 + 80 + 4 = three thousand five hundred eightyfour
(vi) 5167 = 5000 + 100 + 60 + 7 = five thousand one hundred sixtyseven
The digits of a number express their own values when the number is given in expanded form and read in words. The value of a digit, when expressed in the expanded form of the number, is called the place value in the number.
For example:
(i) In 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 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 of a digit in a number is the value it holds for the place in the number. If 5 is in a thousand places, its place value is 5000, if it is a hundred places, its value is 500, and so on.
In number 2137, 2 is in a thousand, 1 in a hundred, 3 in ten and 7 in that place. The place values of the digits 2, 1, 3 and 7 are therefore 2000, 100, 30 and 7.
Place the value of a digit = digit × position of the digit
For example,
(i) The place value of 7 in 3765 is 7 × 100 = 700 or 7 hundred.
(ii) The place value 9 in 9210 is 9 × 1000 = 9000 or 9 thousand.
(iii) The place value of 4 in 5642 is 4 × 10 = 40 or 4 tens.
Now let’s find the place value of each digit of the numbers given below.
(i) 5672; (ii) 4198
(i) 5672
At number 5672
The place value of 5 is 5000 (in words five thousand)
The place value of 6 is 600 (in words six hundred)
The place value of 7 is 70 (in words seventy)
The place of 2 is 2 (in words two)
(ii) 4198
At number 4198
The place value of 4 is 4000 (in words four thousand)
The value of 1 is 100 (in words one hundred)
The place value of 9 is 90 (in words ninety)
The place value of 8 is 8 (in words eight)
The face value of a digit is the digit itself, in whatever position. It is immutable and unique. However, the place value changes depending on the place of the number.
For the example; to find the 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 nominal value as well as the place value of zero (0) is always (0).
We used the Spike Abacus to correctly show, read, and write a number. Now that we know the values of the digits, let’s read and write the numbers without the help of an abacus.
This abacus shows the number 423.

After the abacus, 4 pearls are at the Hposition (hundreds place) 2 pearls are at the Tdigit (tens digit) 3 pearls are with you Hence the number = 400 + 20 + 3 = 423 
Now that we know the face value and place of the digit, let’s find the total value of a number. how:
In 423;
The face value of 4 is 4 and the place value of 4 is 400
The face value of 2 is 2 and the place value of 2 is 20
The face value of 3 is 3 and the place value of 3 is 3
So, 423 = 400 + 20 + 3
It is read as four hundred, twenty three, or four hundred twenty three.
The nominal value of a digit is the digit itself. The nominal value of a digit is unchangeable and unique. However, the place value changes depending on the place of the number.
For example, a face value of 5 in 3547 is 5 and in 8599 is also 5.
Likewise face value of 7 in 27th36 is 7.
Now let’s find the face value and the place value of all the digits in angel number 9283.
The face value 3 is 3 and the place value 3 is 3.
The face value 8 is 8 and the place value 8 is 80.
The face value 2 is 2 and the place value 2 is 200.
The face value 9 is 9 and the place value 9 is 9000
3rd grade math lesson
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