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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.

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• 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...

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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.

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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.

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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.

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• Addition and subtraction

Addition and subtraction of decimals are just like addition and subtraction of whole numbers, except that the numbers are lined such that the decimal points are in the same place. If decimals does not have same length then put in zeros so the numbers have the same length. One must take special care while adding decimal with whole number.

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• Multiplication and Division

When you Multiply a decimal by a number, which is a multiple of 10, the decimal point will move to the right one place for every 0 in that number.

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When you Divide a decimal by a number, which is a multiple of 10, the decimal point will move to the left one place for every 0 in that number

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While multiplying decimals just multiply numbers normally but in the end put the decimal point in the answer. The answer will have as many decimal places as the two original numbers have decimal places in combined. In another word just count up how many numbers are after the decimal point in both numbers you are multiplying, then the answer should have that many numbers after its decimal point.