Percentages and fractions are part of our every day lives, but did you know you can write percentages and fractions, and fractions as percentages? For example, you probably know that $\frac{1}{2}$12 is the same as a half, or $50%$50%, but WHY?
Every percentage can be thought of as a fraction with a denominator of $100$100. In fact, that's what the percent sign means! Doesn't it look like a strange mixed up little $100$100, or even a fraction with a $0$0 on top and and a $0$0 on bottom? Even cooler is the fact that the word percent actually comes from per centum, which is Latin for per one hundred! For example, $3%$3% would mean $3$3 per $100$100, which is a fancy way of saying $3$3 out of $100$100. This is why we can write it as the fraction $\frac{3}{100}$3100, which is ALSO like saying $3$3 out of $100$100.
So to convert any percentage to a fraction all you have to do is to take the number in front of the percent sign and put it as the numerator of a fraction with a denominator of $100$100, or in other words, divide by $100$100.
But how did we go from $50%$50% to $\frac{1}{2}$12? Well, using what we just learnt, $50%=\frac{50}{100}$50%=50100. Can you see that we can simplify this fraction by dividing top and bottom by $50$50? $50\div50=1$50÷50=1, and $100\div50=2$100÷50=2, so $\frac{50}{100}=\frac{1}{2}$50100=12, voila!
$33\frac{1}{3}$3313% and $66\frac{2}{3}$6623% are special percentages, can you guess what they'll be as fractions? Try and put $\frac{1}{3}$13 and $\frac{2}{3}$23 into your calculator and seeing what decimal it becomes! Now try putting those percentages in! That's right, all four values turn into one of two recurring decimals $0.3333$0.3333... and $0.6666$0.6666... So it's important to remember that $33\frac{1}{3}$3313% = $\frac{1}{3}$13 and $66\frac{2}{3}$6623% = $\frac{2}{3}$23, and later you'll learn why that's so when you encounter these strange decimals.
Let's see what happens when we try to convert a fraction that's doesn't convert to a whole number when represented as percentage, for example $\frac{4}{7}$47. Of course let's first follow the usual steps to multiply it by $100%$100% to convert into a percentage. $\frac{4}{7}\times100%=\frac{400%}{7}$47×100%=400%7. Because this is a improper fraction percentage, it's hard to understand it when looking at it straight away, that's why it'll be easier to change it into a mixed fraction, which is $57\frac{1}{7}$5717%. Now we can look at it straight away and understand this is around $57%$57% but a tiny bit over.
Convert $\frac{16}{3}$163 into a percentage
Remember that you can have percentages more than $100$100
Do:
$\frac{16}{3}\times100%$163×100% | $=$= | $\frac{1600%}{3}$1600%3 |
$=$= | $533\frac{1}{3}$53313 $%$% |
Express $\frac{4}{13}$413 as a percentage, rounded to $2$2 decimal places
Think about whether you need to round up or round down
Do
$\frac{4}{13}\times100%$413×100% | $=$= | $\frac{400%}{13}$400%13 | multiply numerators |
$=$= | $30.7692$30.7692 ... $%$% | evaluate | |
$=$= | $30.77%$30.77% | round to $2$2 decimal places |
Fraction → Percentage: multiply by $100%$100%
Convert $\frac{3}{4}$34 into a percentage.
Xanthe and Jimmy are spellchecking an article before it is printed. Xanthe checks $\frac{3}{5}$35 of the article and Jimmy checks $34%$34% of the article.
What percentage of the article have they checked altogether?
What percentage still needs to be checked?