Question

How many degrees are there in $1\dfrac{1}{2}$ turns?

Answer 1

Hint : A turn is a unit which is equal to $2\pi$ radians, ${360^ \circ }$ or $400$ gradians. A turn can also be called a cycle revolution, full circle or complete rotation. According to the question we have to find the degrees from the turns given. So first take out turn for ${1^ \circ }$ and then multiply the turns into the ${1^ \circ }$ value to get the required degree.

Complete step-by-step answer :
We are given a mixed fraction $1\dfrac{1}{2}$ .
In order to convert the turns into degree lets first convert this mixed fraction in the regular fraction of the form $\dfrac{p}{q}$ by using the rule $a\dfrac{x}{y} = \dfrac{{ay + x}}{y}$
In our case we have $x = 1,a = 1\,and\,y = 2$
$1\dfrac{1}{2} = \dfrac{{2\left( 1 \right) + 1}}{2} = \dfrac{{2 + 1}}{2} = \dfrac{3}{2}$
From the unit conversion of turns we know that $1$ turn is equal to $2\pi$ which is equal to ${360^ \circ }$ .
$1$ turn $= {360^ \circ }$
No find the turn for $1\dfrac{1}{2} = \dfrac{3}{2}$ multiply both sides by $\dfrac{3}{2}$ and we get:
$1$ turn$\times \dfrac{3}{2} = {360^ \circ } \times \dfrac{3}{2}$
On further solving we get:
$1$ turn$\times \dfrac{3}{2} = {360^ \circ } \times \dfrac{3}{2}$
$\dfrac{3}{2}$ turns $= \dfrac{{{{1080}^ \circ }}}{2} = {540^ \circ }$
Therefore, there are ${540^ \circ }$ in $\dfrac{3}{2}$ turns that is $1\dfrac{1}{2}$ turns.
So, the correct answer is “${540^ \circ }$”.

Note : We can take out a degree for any turns. Just replace $\dfrac{3}{2}$ with $n$ and similarly for any turns we can convert it into degrees.
If mixed fraction is not given then directly put the value without converting it into simple fraction.
By this method we can convert turns into any units like radians, gradians or degrees.
We can also do vice versa just by dividing the degree obtained by ${360^ \circ }$ .