UNIT 6 Percentage

6.1 Definition.

A percentage is a way of expressing a number, especially a ratio,  as a fraction of 100.

It is denoted using the percent sign, “%”, or the abbreviation “pct.”

45% (forty-five percent - no <s> at the end!) is equal to 45/100 or 0.45.

The fraction 1/2 is expressed as a percentage of 50%.

Note: a small percentage of students vs. a big percentage of students

6.2 Rise or fall in a quantity.

When speaking of a "10% rise" or a "10% fall" in a quantity, the usual interpretation is that this is relative to the initial value of that quantity. For example, if an item is initially priced at \$200 and the price rises 10% (an increase of \$20), the new price will be \$220. Note that this final price is 110% of the initial price (100% + 10% = 110%).

6.3 <Decreased by> vs. <increased by>.

If a number is decreased by 10%, the ratio of the new number to the old number is 90:100.

If a number is increased by 10%, the ratio of the new number to the old number is 110:100.

6.4 Rate of interest.

If we borrow a sum of money at a rate of interest of 10%, we must pay back the money in the same proportion.

6.5 Average percentage.

If a student scores 75% in one exam and 93% in the next, his average (or mean) percentage is 84%.