Like Decimals:
Consider decimal numbers with the same number of decimal places.
For example, consider the decimal numbers 3.42, 6.05, 10.21 and 11.53.
All these decimal numbers have two decimal places.
Let us convert them into decimal fractions.
3.42 = \(\frac{342}{100}\), 6.05 = \(\frac{605}{100}\), 10.21 = \(\frac{1021}{100}\), 11.53 = \(\frac{1153}{100}\)
We observe that the decimal fractions so formed are like fractions.
So, the corresponding decimal numbers 3.42, 6.05, 10.21 and 11.53 are called like decimal numbers or like decimals.
Equivalent Decimals:
Consider the decimal numbers 4.2, 4.20, 4.200, 4.2000. Let us convert them into decimal fractions.
4.2 = \(\frac{42}{10}\), 4.20 = \(\frac{420}{100}\), 4.200 = \(\frac{4200}{1000}\), 4.2000 = \(\frac{42000}{10000}\)
We observe that \(\frac{42}{10}\), \(\frac{420}{100}\), \(\frac{4200}{1000}\), \(\frac{42000}{10000}\) are equivalent fractions.
So, the corresponding decimal numbers 4.2, 4.20, 4.200 and 4.2000 are equivalent decimal numbers or equivalent decimals.
Comparing Decimal Numbers:
For comparing two decimal numbers, compare their whole numbers first. A decimal number with the greater whole number is greater than a decimal number having the smaller whole number.
Let us compare 14.62 and 9.81
14.62 > 9.81 because 14 > 9.
If the whole numbers of the two decimal numbers are equal, then start comparing the corresponding digits of the two decimal numbers which fall after the decimal point, from left to right. Let us compare
Here, the two decimal numbers have their whole numbers equal. The first decimal place digit is also the same. So, compare the second decimal place digits.
2 < 3. So, 20.629 < 20.635.