# Decimal Fraction

A decimal fraction is an ordinary fraction whose denominator is a unit followed by zeros.

For instance.  310,47100,1110000310,47100,1110000

Such fractions are usually written without a denominator , and the meaning of each digit depends on the place in which it stands. For such fractions, the integer part is separated by a comma, and after the comma there should be as many digits as there are zeros in the denominator of the ordinary fraction. The digits of the fractional part are called decimal places.

For instance.  21100=0,21;321100=3,2121100=0,21;321100=3,21

The first decimal place after the decimal point corresponds to the tenth, the second to the hundredth, the third to the thousandth, etc.

If the number of zeros in the denominator of the decimal fraction is greater than the number of digits in the numerator of the same fraction , then after the decimal point, the required number of zeros is added in front of the numerator digits.

Since there are four zeros in the denominator, and two digits in the numerator, we add in the decimal notation of the fraction before the numerator 4−2=24−2=2 zero.

## Basic decimal property

Property

If we add a few zeros to the decimal fraction on the right, then the decimal fraction will not change.

For instance.  12,034=12,0340=12,03400=12,034000=…12,034=12,0340=12,03400=12,034000=…

Comment

Thus, zeros at the end of a decimal fraction are not taken into account, therefore, when performing various actions, these zeros can be crossed out / discarded.

## Decimal Comparison

To compare two decimal fractions (to find out which of the two decimal fractions is greater), you need to compare their integer parts, then tenths, hundredths, etc. If the integer part of one of the fractions is larger than the integer part of the other fraction, then the first fraction is considered larger. In the case of equality of whole parts, the fraction with the tenths more, etc. is greater.

Example

The task. Compare fractions2,4322,432 ; 2,412,41 and 1,2341,234

Decision. Fraction1,2341,234 is the smallest, since its integer part is 1, and 1<21<2 where 2 is the integer part of the two remaining fractions 2,4322,432 and 1,2341,234 .

Now compare the size of the fraction 2,4322,432 and 1,2341,234. Their integer parts are equal to each other and equal to 2. Compare tenths:4=44=4. Compare the hundredths:3>13>1. In this way, 2,432>2,412,432>2,41 .

So, finally we have: 1,234<2,41<2,4321,234<2,41<2,432

Answer.   1,234<2,41<2,432