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# How do you convert $200$ into $\pi$ Radian?

Last updated date: 14th Sep 2024
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Hint: We are given a number as $200$ degree. We have to convert it into radian to do so we will learn about the relation between the degree and radian, we will use the relation into degree $=\pi$ radian on we say $\pi$ radian $=180{}^\circ$ to solve our problem, we will use the unitary method to find the value of the given value.

Complete step-by-step solution:
We are given a $200$ degree and we are asked to convert it to a degree. Before.
For we start, we will learn that dimensional analysis is a method which helps us convexity the term from one dimension to answer dimension which actually changes the value of the quantity.
For example, we know that a meter is the same as $100\,cm$, here quantity is same but dimensions are different.
So, we will use dimensional analysis, we will look at the relation between degree and the radian.
$180{}^\circ =\pi$ radian
Or
We may unit this as
$\pi \,radian=180\,degree\,$
Now we will use a unitary method to find the value of degree or radian and use it further.
Now as we know that
$\Rightarrow 180\,\text{degree}$ is same as $\pi$ radian
So, by unitary method, degree will be given as
$1\,\text{degree=}\dfrac{\pi }{180}\text{radian}............\text{(i)}$
Now we have to find the value of $200$ degree so since we have value of $1\,\,\text{degree}$ as $\dfrac{\pi }{180}$, so value of $200$ degree will be achieved by multiply $\dfrac{\pi }{180}$by $200$
Hence multiply equation (i) by $200$
We get $\Rightarrow 200\,\text{degree=}\dfrac{\pi }{180}\times 200$
Now we simply we get
$200\,\text{degree=}\dfrac{\pi \times 10}{18}$
$\dfrac{5\pi }{9}$
So we get $200\,\text{degree=}\dfrac{5\pi }{9}\,radian$
Hence our $20\,\text{degree}$is the same as $\dfrac{5\pi }{9}$radian.

Note: We need not to change $\pi$ into $\dfrac{22}{7}$ form, as mostly it will get canceled in the process and we can wait till the last moment. We don’t directly start multiplying term in numerator or denominator because it will get long while we stay put and cancel as much as possible in numerator and denominator, also remember unitary method always helps in finding the value of “n” items if we know the value of them.