Video Transcript
The ratio one to π is equivalent to 0.8 to four. What is the value of π?
Weβve been given two equivalent ratios. And one way to solve this would be to write these values as fractions and set them equal to each other. 0.8 to four can be written as 0.8 over four. And weβll write one to π as one over π. We can now think, how do we go from 0.8 to one?
We know that anything divided by itself is equal to one, and that means 0.8 divided by 0.8 equals one. And when weβre working with fractions and ratios, what we do to the numerator we need to do to the denominator. π must be equal to four divided by 0.8. And if we divide four by 0.8, we get five. And that means our π-value should be equal to five.
But what if you didnβt think of dividing 0.8 by 0.8? We could use a different strategy. We could try to get rid of this decimal in the numerator. We know that 0.8 is eight-tenths. And we can write that as the fraction eight over 10. And that fraction can be reduced by dividing the numerator and the denominator by two. Eight-tenths is equal to four over five. And this means our ratio is four-fifths over four. And we know four-fifths divided by four is equal to four-fifths times one-fourth. And when weβre multiplying fractions, we can cancel out these fours so that our ratio, 0.8 over four, is equal to one over five. This means the ratio is one-fifth is equal to one over π and confirms that π equals five.
