It’s Professor Dave, let’s do some conversions.
We’ve learned about fractions, decimals, and percentages, and we’ve seen how we can
use any of these to represent the same value, so we certainly must be able to convert between
these different ways of representing numbers.
Let’s take something like thirty percent.
It’s very easy to convert this to a fraction, because we know that percentages are out of
a hundred, so thirty percent becomes thirty one-hundredths, or thirty out of a hundred.
Then, to reduce the fraction, we can divide both numbers by ten, and here’s a hot tip,
when we do this, we can just cross out the zero in each number, as that will do the same
thing as dividing by ten.
That leaves us with three tenths.
So thirty percent is equivalent to three tenths.
Now let’s get that as a decimal.
Well we know where the tenths place is, so if we have three tenths, we just need to place
a three in the tenths place, so zero point three.
And there we have three different ways of expressing the same value.
Here’s another hot tip, when converting from percentages directly to decimals, all
we have to do is move the decimal place twice to the left, because one hundred is two orders
of magnitude greater than one.
So from thirty percent, we just take the decimal place, which isn’t written but is implied
to be just to the right of the units place, and move it over twice to the left.
We can never start a number with a decimal point, there has to be a zero first, so that
gives us zero point three.
We could do the same with an eight point two five percent sales tax.
We move it once, and then if we have to move it again but there are no more numbers, just
put a zero.
And there we have zero point zero eight two five, or the sales tax expressed as a decimal.
This is useful, because if you want to compute the sales tax on an item, you can just multiply
its price by this number, so a fifty-dollar shirt would have a sales tax of four dollars
and thirteen cents.
To go from a decimal to a percentage, we just move the decimal twice to the right, because
this is the same thing as multiplying by a hundred.
So 0.84 becomes eighty-four percent.
To go from a fraction to a percent, we could convert the fraction into a decimal first.
For three fifths, first we can ask, what is one-fifth as a decimal?
That would be zero point two, because five of these, or five fifths, would add up to
one.
So three fifths must be zero point six.
From there, we just move the decimal over twice, adding a zero since we need to, and
we get sixty percent.
Here is a table with some common fractions, and their corresponding values as decimals
and percentages.
We should be able to convert between these forms with ease, as these are all just different
ways of communicating ideas that are useful in different scenarios.
Let’s try and put this to use.
Here are three values, forty-five percent, twenty-one fiftieths, and zero point four
three.
Let’s try to arrange these from least to greatest.
Well forty-five percent is the same as forty-five over a hundred.
What should we do with this fraction?
Well if we want to compare it to another fraction, it needs to have a hundred in the denominator,
so let’s get this one looking that way too.
Multiplying both numbers by two, we get forty-two over a hundred.
And with the final value, we can move the decimal over twice to get forty-three percent,
which must be forty-three over a hundred.
Now it is quite easy to put them in order, because they look the same.
Forty-two comes first, then forty-three, then forty-five.
That means that this will be the correct order for the original values.
Let’s check comprehension.