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Introduction to Decimals

Decimals Fractions:- in free algebra help ,A fraction whose denominator is 10 or some positive integral power of 10, is called a decimal fraction.

For example, $\frac{3}{10}$, $\frac{47}{100}$, $\frac{528}{1000}$, $\frac{4286}{1000}$, etc

These decimal fractions can be written in the decimal form as : 0.3, 0.47, 0.528, 4.286, etc

Decimals:- The numbers written in the decimal form are called decimal numbers or simply decimals.

Thus, each of the numbers 0.3, 0.47, 0.528, 4.286

A decimal has two parts: Whole number part and Decimal part

These parts are separated by a dot (.), called decimal point. The digits lying to the left of the decimal point form the whole number part. The decimal point together with the digits lying to its right form the decimal part.

Example. In the decimal number 328.745, we have :

Whole number part = 328 and Decimal part = .745

Decimal Places

The number of digits contained in the decimal part of a decimal given the numbe of its decimal places

Example:- (i) 2.75 has 2 decimal places (ii) 1234.567 has 3 decimal places


Like Decimal

Decimals having the same number of decimal places are called like decimals

Example:- (i) 3.1, 46.3, 1247.5, 437.0 are like decimals, each having 1 decimal places.

(ii) 2.68, 11.54, 0.79, 1.40 are like decimals, each having 2 decimal places.

Unlike Decimal

Some given decimals, all not having the same number of decimal places, are called unlike decimals.

Example:- (i) 4.38 and 43.8 are unlike decimals

(ii) 16.58m 9.637, 0.8 are unlike decimals

Conversion of Unlike Decimals to Like Decimals

Annexing zeroes to the extreme right of the decimal part of a decimal does not change its value.

e.g., 0.9 = $\frac{9}{10}$ = $\frac{90}{100}$ = 0.90 and 0.90 = $\frac{90}{100}$ = $\frac{900}{1000}$ = 0.900

... 0.9 = 0.90 = 0.900, etc

Procedure

Step1:- out of given unlike decimals find the decimal which has the largest number of decimal places,

say n.

Step2:- convert each decimal into the one having n decimal places places by annexing the required

number of zeroes to the extreme right of the decimal part. Thus, all the given unlike decimals

are converted to like decimals.

Example. Convert the decimals 0.683, 8.75, 9.6, 6.01 into like decimals

Solution. The decimal 0.683 has the largest number of decimal places, i.e., 3. So we convert each of

the given decimals into the one having 3 decimal places. Thus we write :

Clearly, 0.683, 8.750, 9.600 and 6.010 are like decimals

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