CLASS-5
DECIMAL-SOME OTHER WAY OF INTRODUCTION

 DECIMAL NUMBERS -

A decimal number is a number that is expressed using the base-10 numeral system. It is also commonly referred to as a "real number" or a "base-10 number." The base-10 system uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent any numerical value.

In a decimal number, the position of each digit determines its value. The rightmost digit represents the units place, the next digit to the left represents the tens place, then hundreds, thousands, and so on. Each digit's value is obtained by multiplying the digit by the corresponding power of 10.

For example, in the decimal number 456.78:

• The digit 4 is in the hundreds place and represents 4 x 10^2 (or 4 x 100), which equals 400.
• The digit 5 is in the tens place and represents 5 x 10^1 (or 5 x 10), which equals 50.
• The digit 6 is in the units place and represents 6 x 10^0 (or 6 x 1), which equals 6.
• The digit 7 is in the tenths place and represents 7 x 10^(-1) (or 7 x 0.1), which equals 0.7.
• The digit 8 is in the hundredths place and represents 8 x 10^(-2) (or 8 x 0.01), which equals 0.08.

Thus, the decimal number 456.78 can be interpreted as the sum of its individual digit values: 400 + 50 + 6 + 0.7 + 0.08 = 456.78.

A decimal fraction is a fraction whose denominator is 10 or multiples of 10 (i.e. 10 or 100 or 1000 etc.)

                           18

Examples.1)  -------- = expressed as 0.18,

                  100

                          127

Example.2)  -------- = expressed as 0.127,

                1000

                    9

Example.3)  5 ------- = expressed as 5.9, etc. are decimal fraction 

                   10

Points To Remember:-

1) The number of digits after the decimal point is equal to the number of zeroes in the denominator of the fraction.

2) A decimal point separates a whole number from a decimal fraction.

3) The digits after the decimal point are read one by one.

                            8

Examples: a) ------- = is expressed as 0.08 and is read as zero point

                          100                                             zero eight.

              27

b) 12 ------ is expressed as 12.27 and is read as twelve point two seven

             100

and not as twelve point twenty seven.