Decimals, Ratios and Percents

Decimals continue the place value notation to values smaller than a whole number. Adding a decimal point after the ones place means that the numbers to the right of the decimal point: the number of tenths, hundredths, thousands, etc. are added to the whole number to the left of the decimal point.

Decimals are another way to describe fractions of a whole.

For example, the number 15.23 represents:

15 plus 2 tenths and 3 hundredths.

Ratios always relate two or more groups. If you have a ratio of 2:3, it means that the total number of groups is 5 (or a multiple of 5) and that the proportion or fraction of one group does not change in comparison to the other groups. A ratio of 2:3 could mean that you plant 2 maple trees for every 3 oak trees in a park. If you have a large park, you might plant 40 maple trees and 60 oak trees, but the ratio will be the same. 40 % of the trees will be maple trees.

Ratios are another way to express the percent of one group with respect to the whole. You can also use ratios to relate more groups. If you added birch trees, you might have a ratio of 2:3:1, with the total being a multiple of 6. In this case 2 out of 6 trees would be maple, which is 1/3 or 33.3% of the trees.

Ratios are like recipes. If you double the lemonade recipe because you are going to sell lemonade on a hot day, you will keep the ratio of ingredients the same, but double the amount of each ingredient. If you forget to double the amount of sugar, the recipe ratio will be wrong and may taste very sour!

Percents are written either as a fraction, where the fraction is always out of 100 (4/10 = 40/100), or as a decimal between 0.00 - 1.00 (0.40). The picture above represents 40% (40/100 or 0.40). The percent sign means to use the whole number as a fraction of 100 or divide by 100 and write the decimal.

The most useful phrase for calculating percents is "percent of", which means multiply the fraction or decimal by the number you are taking a percentage of.

40% of a year is 0.40 * 365 days = 146 days

You can also rearrange the numbers for the reverse problem. Percent of a whole is a part.

Whole = part divided by percent

where percent is expressed as a decimal

For example:

3 months is what percent of a year?

12 months = 3 months / percent

So, percent = 3 months / 12 months which is

percent = 1/4

percent = 0.25 or

25 %