Nov 26, 2015 · $\begingroup$ In fact, both $\frac{22}{7}$ and $\frac{355}{113}$ are the second and fourth rational approximations of $\pi$ in a sequence of approximations called convergents of $\pi$, and they are in a sense that can be made precise "as good as possible". One can compute them quickly using truncations of the continued fraction $[3; 7, 15, 1 ...

But $\pi$ is an irrational (even transcendental) number, so is certainly not equal to the rational number $\frac{22}{7}.$ The calculation of $\pi$ to any desired degree of accuracy is the subject of much mathematics, and I am sure you will receive informative answers here. $\endgroup$ –

Here is a proof that $\displaystyle \frac{22}{7}$ is a better approximation than $\displaystyle 3.14$. First we consider the amazing and well known integral formula for $\displaystyle \frac{22}{7} -\pi$ (for instance see this page: Proof that 22/7 exceeds pi ).

If the circumference of a circular sheet is 154 m, find its radius. Also, find the area of the sheet. (Take π=22/7). The circumference of circle is product of the constant π and the diameter of circle. Radius and area of the circular sheet are 24.5 m2 and 1886.5 m2 respectively.

Sep 29, 2015 · Note too that one can quickly a get cheap but good lower bound on $\pi$ by comparing with a similar function: $$\frac{22}{7} - \pi = \int_0^1 \frac{x^4 (1 - x)^4}{1 + x^2} dx < \int_0^1 x^4 (1 - x)^4 dx = \frac{1}{630} .$$ Rearranging gives that $$3.14126 \ldots = \frac{1979}{630} < \pi < \frac{22}{7} = 3.14285 \ldots ,$$ and using the midpoint ...

Jul 8, 2020 · Yes, $22/7$ is the best. You can check this by directly computing (as suggested in comments to your question) all ratios with numerator to $200$ and denominator up to $50$ (thus all ratios below $4$) using the short Julia script

22/7 in a mixed fraction is 3 1/7. What is 22/7 as a Mixed Number? 22/7 is an improper fraction. Let us represent it as a whole number as well as a fractional part called the mixed number.

Nov 29, 2014 · I've heard that $\pi$ is usually approximated as 3.14, but it can also be approximated as 22/7, which is equal to 3.142857142857142857....

Find the circumference of the circles with the following radius: (Take π =22/7) (a) 14 cm (b) 28 mm (c) 21 cm. The circumference of a circle is product of the constant π and the diameter of the circle. (a) The radius is 14 cm and circumference is 88 cm, (b) The radius is 28 mm and circumference is 176 mm, (c) The radius is 21 cm and circumference is 132 cm.

Class 9 Maths NCERT Solutions Chapter 13 Exercise 13.3 Question 2. Summary: It is given that the slant height of a cone is 21 m and diameter of the base is 24 m.