Writing approximation symbol(≈) in LaTeX

Approximation symbol

\approx
\approx
\thickapprox
\thickapprox

Let’s see some examples with approximation symbol

Approximations between metric and imperial units

8km\approx 5miles
8km\approx 5miles
1m \approx 40\thinspace inches
1m \approx 40\thinspace inches
\Pi \approx 3.14
\Pi \approx 3.14
30cm \approx 1foot
30cm \approx 1foot
2.5cm\approx 1\thinspace inch
2.5cm\approx 1\thinspace inch
1kg\approx 2.2 \thinspace lbs
1kg\approx 2.2 \thinspace lbs
1 litre\approx 1{3 \over4}\thinspace pints
1 litre\approx 1{3 \over4}\thinspace pints
1gallon \approx 4{1 \over2}\thinspace litres
1gallon \approx 4{1 \over2}\thinspace litres
1\thinspace acre \approx {2 \over5}\thinspace hectare
1\thinspace acre \approx {2 \over5}\thinspace hectare
450g \approx 1 b
450g \approx 1 b

Basic linear approximations

\displaystyle \frac{1}{x-1} \approx 1+x,\qquad  for \thinspace x \approx 0
\displaystyle \frac{1}{x-1} \approx 1+x,\qquadfor\thinspace x \approx 0
(1+x)^r \approx 1+rx , \qquad for \thinspace x \approx 0;\qquad r is any real number
(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;
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
\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
(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;
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{2} \approx 1.414
\sqrt{\frac{(51.3)}{0.53}} \approx \sqrt{\frac{(50)}{0.5}}=\sqrt{100}=10
\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{(4.98)^2}{0.482}\approx \frac{(5)^2}{0.5}
\frac{(565.11022)}{4434.88978}*100 \%\approx 12.74\%
\frac{(565.11022)}{4434.88978}*100 \%\approx 12.74\%

Mohammed Anees

Hey there, welcome to aneescraftsmanship I am Mohammed Anees an independent developer/blogger. I like to share and discuss the craft with others plus the things which I have learned because I believe that through discussion and sharing a new world opens up

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