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Welcome to our Math lesson on Definition of Percentages, this is the first lesson of our suite of math lessons covering the topic of Definition of Percentages, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Definition of Percentages
So far, we have expressed non-whole amounts in two ways: as fractions and as decimals. Percentages on the other hand, represent a third method of expressing amounts.
The term "percent" has a Latin origin. It is translated as "out of 100." Therefore, a percentage represents a certain amount out of 100.
For example, if one says "I got 78% in the exam", the listeners realize that the speaker has got 78 correct out of 100 points available in an exam. This means that 78% is equivalent to 78 out of 100 or 78/100 or 0.78.
Decimal fractions can be written as a percentage only after having expressed them as fractions with denominator of 100. This is the same for decimals as well. A decimal is written as a percentage only after having expressed it at two decimal places (up to hundredths). The only calculation required is multiplying the numerator of the decimal fraction or the decimal itself by 100, i.e.:
ab/100 = 0.ab = ab %
where a represents the tens of ab while b represents the units.
Example 1
Express the following amounts as percentages.
- 0.9
- 1.38
- 34/100
- 3/4
Solution 1
- We have to express the number 0.9 as a fraction with denominator 100. Thus, using the known methods of decimal-fraction conversion, yields
0.9 = 9/10 = 9 × 10/10 × 10 = 90/100 = 90%
- Again, we use the same procedure as in (a), i.e.
1.38 = 138/100 = 138%
- Now, the fraction is ready for conversion into a percentage as it has the denominator 100 already. Thus,
34/100 = 34%
- The fraction 3/4 needs to be converted into fraction with denominator 100 first. Thus,
3/4 = 3 × 25/4 × 25 = 75/100 = 75%
More Definition of Percentages Lessons and Learning Resources
Percentages Learning Material| Tutorial ID | Math Tutorial Title | Tutorial | Video
Tutorial | Revision
Notes | Revision
Questions |
|---|
| 5.1 | Definition of Percentages | | | | |
| Lesson ID | Math Lesson Title | Lesson | Video
Lesson |
|---|
| 5.1.1 | Definition of Percentages | | |
| 5.1.2 | Writing a Number as a Percentage of another Number | | |
| 5.1.3 | Finding the Percentage of an Amount | | |
| 5.1.4 | Calculating the Percentage of another Percentage of an Amount | | |
| 5.1.5 | Operations with Percentages | | |
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- Continuing learning percentages - read our next math tutorial: Percentages, Fractions and Decimals
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