#### 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\thinspace x \approx 0
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;

\displaystyle \frac{1}{x-1} \approx 1+x+x^2,\qquad for \thinspace x \approx 0
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;

#### 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\%

### 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