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Decimal Numbers
The word 'decimal' means based on 10'. This word has been derived from the Latin word decima meaning a tenth part.
The fractional numbers having denominators 10,100,1000, etc. are called decimal fractions or decimals.
Definition of Decimal Numbers:
We have learnt that the decimals are an extension of our number system. We also know that decimals can be considered as fractions whose denominators are 10, 100, 1000, etc. The numbers expressed in the decimal form are called decimal numbers or decimals.
For example: 5.1, 4.09, 13.83, etc.
A decimal has two parts:
(a) Whole number part
(b) Decimal part
These parts are separated by a dot ( . ) called the decimal point.
• The digits lying to the left of the decimal point form the whole number part. The places begin with ones, then tens, then hundreds, then thousands and so on.
• The decimal point together with the digits lying on the right of decimal point form the decimal part. The places begin with tenths, then hundredths, then thousandths and so on………
For example:
(i) In the decimal number 211.35; the whole number part is 211 and the decimal part is .35
It can be arranged in the place-value chart as:
(ii) In the decimal number 57.031; the whole number part is 57 and the decimal part is .031
(iii) In the decimal number 197.73; the whole number part is 197 and the decimal part is .73
Some decimal fractions are expressed as given below:
(i) \(\frac{4}{10}\) is expressed as 0.4
(ii) \(\frac{7}{10}\) is expressed as 0.07
(iⅲ) 5\(\frac{17}{100}\) is expressed as 5.17
The 'dot' '.' is called the decimal point.
Therefore, decimal fraction consist of two parts
i,e. whole number part and decimal part, and they are separated by the decimal point.
Note:
1. 3.5 is read as 'three point five'
2. 5.71 is read as 'five point seven one'
3. 10.01 is read as 'ten point zero one'
4. 6.40 is read as 'six point four zero'
● Related Concept
● Decimals
● Conversion of Unlike Decimals to Like Decimals
● Decimal and Fractional Expansion
● Converting Decimals to Fractions
● Converting Fractions to Decimals
● H.C.F. and L.C.M. of Decimals
● Repeating or Recurring Decimal
● BODMAS/PEMDAS Rules - Involving Decimals
● PEMDAS Rules - Involving Integers
● PEMDAS Rules - Involving Decimals
● BODMAS Rules - Involving Integers
● Conversion of Pure Recurring Decimal into Vulgar Fraction
● Conversion of Mixed Recurring Decimals into Vulgar Fractions
● Rounding Decimals to the Nearest Whole Number
● Rounding Decimals to the Nearest Tenths
● Rounding Decimals to the Nearest Hundredths
● Simplify Decimals Involving Addition and Subtraction Decimals
● Multiplying Decimal by a Decimal Number
● Multiplying Decimal by a Whole Number
● Dividing Decimal by a Whole Number
● Dividing Decimal by a Decimal Number
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