Decimals

• Defination for Decimals

The decimal numeral system (also called base ten or occasionally denary) has ten as its base.

To understand decimal numbers you must first understand place value

We have learnt place value for Whole numbers, same theory apply to decimal numbers too.

• Comparing Decimals

To compare two decimals, begin from left to right

Example 34.123 and 34.113

Ones and tens : Both numbers have the digit 3 in the tens and 4 in the ones.

Tenths : Both numbers have the digit 1 in the tenths place.

Hundredths : The digit 2 is greater than 1 . Therefore 34.123 is greater than 34. 113 .

• Converting Fractions into Decimals

It is easy to convert fraction into decimal, when it's denominator is either 1s, 10s , 100s or any 1 followed by 0s.

• When the denominator of the fraction is 10, the decimal it is conveted to has 1 place decimal.

• When the denominator of the fraction is 100, the decimal it is converted to has 2 place decimal.

• When the denominator of the fraction is 1000, the decimal it is converted to has 3 place decimals and so on...

To convert fraction, whose denominator is not 10s, 100s , 1000s or any 1 followed by 0s, we have to multiply the fraction with the number that convert the denominator into 10s, 100s , 100s 0r any 1 followed by 0s.

With some fractions it's not possible to convert denominator into 10s, 100s or 1000s, in such cases;

We have to multiply the fraction with the number that round off the denominator to the nearest tenth, the hundredth or thousandths.

Note: It is preferable, in such cases first apply division of the fractions and then round it off to nearest 10th, 100th or 1000th

• Converting Decimals into Fractions

To convert decimals into fractions, first of all count the number of decimal places, if there is 1 place decimal then denominator is 10; if 2 place decimal then denominator is 100; and if 3 place decimal then denominator is 1000 so on; then according to that convert decimals into fractions and simplify them.