# Fractions, decimal numbers and percent

How many hundredths is $\frac{30}{50}$?

## Fractions, decimal numbers and percent

​ ​Leon and Lena are in Tanzania on a safari. On the first day, they see 50 animals - 18 gazelles, 15 zebras, 10 elephants, 7 giraffes. What percentage of these animals are elephants? 10 out of 50 animals are elephants. The percentage can be written as a fraction with the part, the number of elephants, in the numerator, and the whole, the number of animals, in the denominator.

The part is 10 and the whole is 50. The percentage or share is then ten fiftieths. When you want to know the percentage, you write a fraction with the part in the numerator and the whole in the denominator. Here we can simplify the fraction, dividing both the numerator and the denominator by ten. In the numerator we get 10 divided by 10 equals 1, and in the denominator we get 50 divided by 10 equals 5.

Therefore elephants make up one fifth of all animals if we give the answer as a fraction. Since we write the the fraction with the smallest possible denominator, our answer is in the simplest form. ​ ​Now what percentage of all animals are elephants? In the fraction form the answer is 10 over 50, or one fifth. Beginning with 10 over 50, it's easy to convert the fraction into hundredths. We simply multiply both the numerator and the denominator by two.

In the the numerator we get 10 times 2 equals 20, and in the denominator we get 50 times 2 equals 100. When we multiply both the numerator and the denominator by the same number, we expand the fraction without changing its value. You remember that one hundredth is equal to 1%, right? So 20 divided by 100 is equal to 20%. ​ ​The following day they see even more animals, 72 in total - 22 gazelles, 19 zebras, 13 giraffes, 9 lions, 7 rhinos, and 2 leopards. What share of these animals are lions?

Nine out of 72 animals are lions. In the fraction form we write 9 divided by 72. Here, we simply the fraction by dividing both the numerator and the denominator by nine. In the numerator, we get 9 divided by 9 equals 1, and in the denominator we get 72 divided by 9 equals 8. Therefore the lions make up one eighth of all animals, stated as a fraction in the simplest form. ​ ​Now, how many percent of all animals are lions?

Maybe you can figure out how many percent is one eighth, if you recall that one eighth is half of one fourth. Too hard? Well, it's not easy to expand or simplify this fraction to get 100 in the denominator. Instead we have to divide 1 by 8. Use your calculator and you'll see that the answer is 0.125.

Do you remember that 0.01 is equal to 100 or 1%? Then 0.125 is equal to 12.5 hundredths or 12.5%. What share of these animals are giraffes? Thirteen out of 72 animals are giraffes. As a fraction we write 13 divided by 72.

Again, it is not easy to simplify or expand this fraction to have 100 in the denominator. Instead divide the numerator by the denominator. Your calculator will tell you that 13 divided by 72 is 0.1805555. Because the quotient is a decimal with many digits, you need to round it, for example, to two decimal places, which gives us 0.18, 18 hundredths, or 18 divided by 100 is equal to 18%. When you want to know the share as a percentage, you write a fraction with the part in the numerator and the whole in the denominator.

A share can be written in a fraction, decimal, or percent form.