Approximation symbol
\approx
\thickapprox
Let’s see some examples with approximation symbol
Approximations between metric and imperial units
8km\approx 5miles
1m \approx 40\thinspace inches
\Pi \approx 3.14
30cm \approx 1foot
2.5cm\approx 1\thinspace inch
1kg\approx 2.2 \thinspace lbs
1 litre\approx 1{3 \over4}\thinspace pints
1gallon \approx 4{1 \over2}\thinspace litres
1\thinspace acre \approx {2 \over5}\thinspace hectare
450g \approx 1 b
Basic linear approximations
\displaystyle \frac{1}{x-1} \approx 1+x,\qquad
(1+x)^r \approx 1+rx ,\qquad for \thinspace x \approx 0; \qquad r is any real number
sin \thinspace x\approx x , \qquad for \thinspace x \approx 0;
Basic quadratic approximations
\displaystyle \frac{1}{x-1} \approx 1+x+x^2,\qquad for \thinspace x \approx 0
(1+x)^r \approx 1+rx + \frac{r(r-1)}{2} x^2, \qquad for\thinspace x \approx 0; \qquad r is any real number
cos x \thinspace 1-\displaystyle \frac{x^2}{2}\approx x ,\qquad for\thinspace x \approx 0;
Some more examples of approximations
\sqrt{2} \approx 1.414
\sqrt{\frac{(51.3)}{0.53}} \approx \sqrt{\frac{(50)}{0.5}}=\sqrt{100}=10
\frac{(4.98)^2}{0.482}\approx \frac{(5)^2}{0.5}
\frac{(565.11022)}{4434.88978}*100 \%\approx 12.74\%

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