Subject: Compulsory Maths
The denominators of the fractions which have the power of 10 then such fractions are called decimal fractions. For example,
\(\frac{8}{10}\) = 0.8
\(\frac{13}{100}\) = 0.13
Terminating and Non-Terminating recurring decimal
When a fraction is expressed in decimal and the decimal part is terminated with a certain number of digits, it is called terminating decimal.
\(\frac{1}{3}\) = 0.3333....
\(\frac{1}{6}\) = 0.16666......
\(\frac{8}{7}\) = 1.1428571....
Similarly, when the fraction is expressed in decimal and the decimal part is never terminated it is called non-terminating decimal. For example,
\(\frac{2}{3}\) = 0.666....
\(\frac{7}{9}\) = 0.7777...
\(\frac{6}{7}\) = 0.857114285......
Four Fundamental operations on decimals
Four Fundamental operations on decimals
Add : \(\frac{2}{9}\) + \(\frac{4}{9}\)
\(\frac{2}{9}\) + \(\frac{4}{9}\) =\(\frac{2+4}{9}\) = \(\frac{6}{9}\) =\(\frac{2}{3}\)
Subtract : \(\frac{5}{7}\) -\(\frac{5}{7}\)
\(\frac{5}{7}\) -\(\frac{2}{7}\) =\(\frac{5-3}{7}\) =\(\frac{3}{7}\)
Solve : \(\frac{1}{3}\) + \(\frac{1}{4}\) +\(\frac{1}{6}\)
\(\frac{1}{3}\) +\(\frac{1}{4}\) +\(\frac{1}{6}\) = \(\frac{1×4+1×3+1×2}{12}\)= \(\frac{4+3+2}{12}\) = \(\frac{9}{12}\) =\(\frac{3}{4}\)
Simplify : 2\(\frac{3}{4}\) + 1\(\frac{5}{8}\) -3\(\frac{1}{3}\)
Solution :
2\(\frac{3}{4}\) + 1\(\frac{5}{8}\) -3\(\frac{1}{3}\)
= \(\frac{11}{4}\) + \(\frac{13}{8}\) -\(\frac{10}{3}\)
=\(\frac{11x6+13x3-10x8}{24}\)
=\(\frac{66+39-80}{24}\)
=\(\frac{105-80}{24}\)
=\(\frac{25}{24}\)
=1\(\frac{1}{24}\)
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