Fractions and decimals

Fractions

This section is included because a thorough understanding of how fractions work is essential in calculating dilutions and the rules for manipulating fractions is relevant to working with exponentials.

A fraction is a number between 0 and 1 expressed as two numbers, one divided by the other e.g.

½ is equivalent to 1 divided by 2.

The number on the top line is the numerator and the number on the bottom line is the denominator.

The denominator divides 1 into a number of equal parts, the number of parts being equivalent to the numerical value of the denominator i.e.

½ divides 1 into 2 equal parts.

The numerator determines how many of those equal parts to consider e.g.

1/5 1 fifth part
2/5 2 fifth parts
2/3 2 third parts

There are some rules governing working with fractions

1. Fractions cannot be added or subtracted from one another unless they have the same denominator

1/3 + 1/3 = 2/3

1/6 + 1/3 = 1/6 + 2/6 = 3/6 = ½

1/3 – 1/6 = 2/6 – 1/6 = 1/6

2. To multiply fractions, multiply the numerators together and the denominators together

1/3 x 1/3 = 1/6

2/3 x 3/5 = 6/15

NOTE: when you do multiply fractions you end up with a number which was smaller than either starting number, that is because you are determining a fraction of a fraction

3. To divide fractions you must invert the fraction on the bottom of the equation and then multiply the result

3/5
2/7 = 3/5 x 7/2 = 21/10

Decimals

Another way of expressing a number that is less than 1 is by decimals. Every number has a decimal point after the last integer in the number but the point is not always written down e.g.

1 is actually 1.0
23 is 23.0

You can express a fraction as a decimal by dividing the numerator by the denominator e.g.

2/5 = 2.0 divided by 5 = 0.4

There are some rules governing working with decimals:

1. When you multiply a decimal by 10, you simply move the decimal point one place to the right.

2. When you divide a decimal by 10, you move the point one place to the left.

3. Similarly when you multiply by 100, you move the point two places to the right, and by 1000, three places to the right and so on.

This is so because 100 and 1000 are multiples or powers of 10.  (see section on powers).