Comparison Of Decimal Fractions -

When we compare two decimal fractions, first we compare the whole number part of the fractions. Obviously the decimal fraction with the greater whole number is greater.

In both the decimal fractions, if the whole number part is same or 0, then we compare the decimal fractions by their tenths. If they have the same digits in the tenths place, then we compare them by their hundredths digits and so on.

To compare decimal fractions, you can follow these steps:-

  1. Compare the whole number parts, if any. If one decimal fraction has a greater whole number part than the other, then it is greater overall. For example, 3.7 is greater than 2.9.
  2. If the whole number parts are equal, compare the decimal parts digit by digit from left to right. Start with the digit immediately to the left of the decimal point. (a.) Compare the first digit to determine which decimal fraction is greater. The one with the larger digit is greater overall. For example, in the comparison between 3.25 and 3.15, 3.25 is greater because the 2 is larger than the 1. (b.) If the first digits are equal, move to the next digit to the right and compare them. Continue this process until you find a pair of digits that are different. The decimal fraction with the larger digit in that position is greater overall. For example, in the comparison between 3.456 and 3.435, the digits at the third decimal place (4 and 5) are different. Since 5 is greater than 4, 3.456 is greater overall.
  3. If the decimal parts are equal up to the last digit, but one decimal fraction has additional trailing zeros, the fraction with the trailing zeros is greater. For example, 3.2 is greater than 3.20.

By following these steps, you can compare and determine the relative sizes of decimal fractions.

Example.1)   Fill in the blanks using > or < sign:

a) 0.46 __________ 0.5

0.46 < 0.5      [Since, 4 tenths < 5 tenths]

b) 0.76 __________ 0.09

0.76 > 0.09     [Since, 7 tenths > 0 tenths]

c)  0.009 ___________ 0.04

0.009 < 0.04    [Since, 0 hundredths < 4 hundredths]