Grouping and Ordering of Decimals
Like and Unlike Decimals
Decimals places:
The number of digits in the fractional/ decimal part of a decimal number gives the number of decimal places.
Examples: (i) 5.76 has two decimal places
(ii) 23.458 has three decimal places
(iii)0.95 has two decimal places.
Like Decimals:
Like decimals refers to the decimals having same number of decimal places. In other words, decimals having same number of figures on the right side of the decimal point are known as like decimals.
Example: 7.29, 15.56, 83.99 are like decimals, each having two places of decimal.
Unlike Decimals:
Unlike decimals refers to the decimals having different number of decimal places. In other words, decimals having different number of figures on the right side of the decimal point are known as unlike decimals.
Example: 0.9, 8.37, 4.997 are unlike decimals, since the numbers contain decimal points up to one, two and three places respectively.
Converting Unlike Decimals into Like Decimals
The unlike decimals can be converted into like decimals by adding appropriate number of zeros to the extreme right of decimal part.
Note: The value of a decimal number does not change if more zeroes are added to the extreme right of a decimal.
Example: Convert 0.2, 7.25 and 9.393 to like decimals
Solution: The number of decimal places in 0.2 = 1
The number of decimal places in 7.25 = 2
The number of decimal places in 9.393 = 3
For converting to like decimals, the three given numbers should have same number of decimal places.
Since, we cannot remove any number from a decimal place, we add appropriate number of zeroes to make number of decimal places in each according to the maximum decimal place i.e. 3 in the given case
Thus, 0.200, 7.250 and 9.393 are like decimals.
Comparison/ Ascending and Descending Order
By converting the unlike decimals into like decimals we can compare the figures. Comparing the decimal figures is as simple as comparing any whole number.
For Example:
- Write the following decimal numbers in ascending order:
- 13.01, 13.51, 13.1, 13.001, 13
- 18.23, 14.83, 18.51, 23.55, 15.01
Solution:
- Let us first convert all unlike decimals into like decimals. So the numbers will be:
13.010, 13.510, 13.100, 13.001 and 13.000
Then arrange it in ascending order:
13.000 < 13.001 < 13.010 < 13.100 < 13.510
- As all the numbers are in like decimals, the ascending order arrangement:
14.83 < 15.01 < 18.23 < 18.51 < 23.55
- Write the following decimals in descending order:
- i.89, 35.78, 12.76, 35.67, 100.01
- 0.001, 0.1, 0.309, 0.189, 0.01
Solution:
- As the terms are like decimals, so we can arrange the figures in descending order,
100.01 > 35.78 > 35.67 > 25.89 > 12.76
- As the terms are not in like decimals, we have to convert it into like decimals.
The numbers will be, 0.001, 0.100, 0.309, 0.189, 0.010
The numbers in descending order,
0.309 > 0.189 > 0.100 > 0.010 > 0.001