Place value and Face value

Place value and Face value

         In this section we will learn about Place value and Face value of a digit present in a number.

         Place value of a digit in a number desribes its position in that number. Each digit has a place in a number. When we write a number in general form, the position of each digit is expanded. Those positions are ones, tens, hundreds, thousands, ten thousands and so on.

Face value:-

                          Face value of a digit in a number is equal to the value of the digit itself at whatever place it is situated.

                         In other words, Face value of  a digit is always equal to that digit. In this we didn't see the place of the digit.

face value

Face Value of a digit = digit itself

e.g.- Let's take a number 453, in which we have to find Face value of  underlined digit 5.

  Face value of 5 = 5

we can find face value of rest of the digits of given number-

Face value of 3 =  3

Face value of 4 = 4

Example 2:- Find face value of each digit of number 4893

Solution:- Because face of a digit does not depend on the palce of the digit. so,

                Face value of 3 = 3

                Face value of 9 = 9

                Face value of 8 = 8

                Face value of 4 = 4

Example 3:- Find face value of each digit of number 2019.

Solution:-  Face value of 9 = 9

                Face value of 1 = 1

                Face value of 0 = 0

                Face value of 2 = 2

Place value:- 

                   Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.

                        In other words, Place value of a number is equal to the face value of the digit multiplied by the place it is situated.

place value

Place Value of a digit = Face Value × Place of digit

e.g.- Let's take a number 453, in which we want the place value of underlined digit 5.

  Face value of 5 = 5

  5 is situated at the place of tens position.

so, Place value of 5 in 453 = face value × palce of digit  = 5×10 = 50

We can find the place value of rest of the digits in number-

  3 is situated at the place of ones position.

so, place value of 3 in 453 = face value × place of digit = 3×1 = 3

  4 is situated at the place of hundreds position.

so, palce value of 4 in 453 = face value × place of digit = 4×100 = 400

Place value chart:-

place value chart

Example 2:- Find place value of each digit of number 4893.

Solution:- 3 is at the place of ones. So

                 Place value of 3 = face value × place of digit = 3×1 = 3

              9 is at the place of tens.  So

                  Place value of 9 = face value × place of digit = 9×10 = 90

              8 is at the place of hundreds. So

                  Place value of 8 = face value × place of digit = 8×100 = 800

              4 is at the place of thousands. So

                  Place value of 4 = face value × place of digit = 4×1000 = 4000

Example 3:- Find the place value of each digit of 2019.

Solution:-   9 is at the place of ones. So

                 Place value of 9 = face value × place of digit = 9×1 = 9

              1 is at the place of tens.  So

                  Place value of 1 = face value × place of digit = 1×10 = 10

              0 is at the place of hundreds. So

                  Place value of 0 = face value × place of digit = 0×100 = 000

              2 is at the place of thousands. So

                  Place value of 2 = face value × place of digit = 2×1000 = 2000

Place value of decimal number:-

                                                           Decimal number contains three parts-

(i) Whole part          (number before decimal point)

(ii) Decimal point     (.)

(iii) Decimal part      (number after decimal point)

Decimal Place value chart

decimal place value chart

e.g.- Let's take a number 25.46.

        6 is at the place of hundredths. So

      Place value of 6 = face value × place of digit = 6×1/100 = 6/100 = 0.06

        4 is at the place of tenths. So

      Place value of 4 = face value × place of digit = 4×1/10 = 4/10 = 0.4

        5 is at the place of ones. So

      Place value of 5 = face value × place of digit = 5×1 = 5

        2  is at the place of tens. So

      Place value of 2 = face value × place of digit = 2×10 = 20

Example 2:- Find the place value of number 546.635.

Solution:- Rightmost 5 is at the place of thousandths. So

        Place value of 5 = face value × place of digit = 5×1/1,000 = 5/1,000 = 0.005

              3 is at the place of hundredths. So

        Place value of 3 = face value × place of digit = 3×1/100 = 3/100 = 0.03

              6 in the decimal part is at the place of tenths. So

        Place value of 6 = face value × place of digit = 6×1/10 = 6/10 = 0.6

              6 in the whole part is at the place of ones. So

        Place value of 6 = face value × place of digit = 6×1 = 6

              4 is at the place of tens. So

        Place value of 4 = face value × place of digit = 4×10 = 40

              Leftmost 5 is at the place of hundreds. So

        Place value of 5 = face value × place of digit = 5×100 = 500

Face value of decimal number:-

                                                        We can find face value of digits in a decimal number as we have discussed above-

Face value of a digit = Digit itself

e.g.- Let's take above example 25.46

       Because Face value is independent from place. So

       Face value of 6 = 6

       Face value of 4 = 4

       Face value of 5 = 5

       Face value of 2 = 2

Example 2:- Find the face value of 546.635

Solution:-  Because Face value is independent from place. So

            Face value of rightmost 5 = 5

            Face value of 3 = 3

            Face value of 6 in the decimal part = 6

            Face value of 6 in the whole part   = 6

            Face value of 4 = 4

            Face value of leftmost 5 = 5

Finding Place value (Trick):-

                                                                        If we have trouble in determining the place of a digit, then we can find the place value of digit by concerning some tricks (methods)-

Let's understand this by an example- 8543218954

 We will find the place value of underlined digit 2 by these steps-

Step 1:- Write the digit for which you want to find the place value.

           In 8543218954, we want to find place value of 2.

Step 2:- Count the number of digits which come after the digit, you want to find the place value.

           In 8543218954, we have 5 digits "18954"

Step 3:- Take the number of zeroes you have counted after the digit.

          since there is 5 digits "18954" after 2 . Hence take 5 zeroes after 2.

Now we get  200000.

So Place value of 2 = 200,000

place value of number

Finding place value in decimal number(Trick):-

                                                                                          We can easily find the place value of digit in a decimal number. Follow these steps-

e.g.- Find the place value of underlined digit in number 512.436636

Step 1:- Write the digit for which you want to find the place value.

             In 512.436636, we want to find place value of 6.

Step 2:- Count the number of digits which come before the digit ( you want to find the place value) and after the decimal point.

             In 512.436636, we have three digits "436"

Step 3:- Take the number of zeroes you have counted before the digit and also put the decimal point at the leftmost.

             since there is three digits "436" before 6. Hence we take three zeroes before 6.

        Now we get 0.0006

or

 Write the 'digit/1' following with one more number of zeroes in denominator, you have counted.

        since there is three digits "436" before 6. so we will take four zeroes in the denominator.

        Now we get 6/10000

Hence place value of 6 = 0.0006 = 6/10000

place value of decimal number

Difference between Face value and Place value:-

Difference between place value and face value

Some problems based on Place value and Face value

Finding difference of place value and face value:-

Problem1:- Find the diffenrence of place value and face value of 5 in 6356.

Solution:- because 5 is at the place of tens. So

               Place value of 5 is: 5×10=50

               Face value of 5 is: 5

               Difference = Place value - Face value

                               = 50 - 5

                               = 45

Problem2:- Find the diffenrence of place value and face value of 7 in 534.761

Solution:- Because 7 is at the place of tenths. So

                Place value of 7 is: 7×0.1=0.7

                Face value of 7 is: 7

               Difference(in decimal number)= Face value - Place value

                                                           = 7 - 0.7

                                                           = 6.3

Finding sum of place value and face value:-

Problem1:- Find the sum of place value and face value of 5 in 6356.

Solution:- because 5 is at the place of tens. So

               Place value of 5 is: 5×10=50

               Face value of 5 is: 5

               Sum = Place value + Face value

                               = 50 + 5

                               = 55

Problem2:- Find the sum of place value and face value of 7 in 534.761

Solution:- Because 7 is at the place of tenths. So

                Place value of 7 is: 7×0.1=0.7

                Face value of 7 is: 7

               Sum= Face value + Place value

                      = 7 + 0.7

                      = 7.7

Finding difference of Place value of different digits in different numbers:-

Problem1:- Find the difference of place value of 5 in 762543 and place value of                   4 in 882843.

Solution:- Because 5 is at the place of hundreds in 762543

               Place value of 5 is: 500

              and 4 is at the place of tens in 882843

               Place value of 4 is: 40

               Difference = Place value of 5 -Place value of 4

                               = 500 - 40

                               = 460

Problem2:- Find the difference of place value of 6 and 2 in 9463264.

Solution:- Because 6 is at the place of ten thousands and 2 is at the place of                      hundreds place.

                Place value of 6 is: 60,000

                Place vlaue of 2 is: 200

                difference = Place vlaue of 6 - Place value of 2

                               = 60,000 - 200

                               = 59,800

Some other type of problem:-

Problem3:- How many times the Place value of 3 than Face value in 9773648.

Solution:-  Because, 3 is at the place of thousands.

                Place value of 3 is: 3000

                Face value of 3 is: 3

                Place value/Face value =3,000/3

                                                  = 1,000

                Hence, Place value is 1,000 times more than Face value.