Use the identities to solve the problems based on simplification of decimal. We will make use of these identities in some of the questions related to division of decimals.
Learn the following identities to apply these in simplifying decimal.
(a) (a + b)^{2} = a^{2} + b^{2} + 2abWorkedout examples on simplification of decimal:
Let us observe how to simplify decimals using identities with detailed stepbystep explanation.
Simplify the following:
(a) {(0.9  0.6)^{2}}/{(0.9)^{2}  2(0.9)(0.6) + (0.6)^{2}}Solution:
Let, a = 0.9 and b = 0.6
So, [(a  b)^{3}]/[a^{2}  2(a)(b) + b^{2}]
= (a  b)
Now putting the value of a and b we get,
= 0.9  0.6
= 0.3
Solution:
Let a = 5.8 and b = 2.6
So, we have
= [a^{3}  b^{3}]/[a^{2}  2ab + b^{2}]= 55.48/3.2
= (55.48 × 10)/(3.2 × 10), Multiply both numerator and denominator by 10
= 554.8/32
= 17.3375
Solution:
Let a = 8.65 and b = 4.35
So, we have
= [a^{2}  b^{2}]/(a  b)= a + b
Now putting the value of a and b
= 8.65 + 4.35
= 13
● 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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