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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