What are Fractions, Decimals and Percentages? Give Examples.
A fraction is a part of a whole number. There are various types of fractions. For example, three-quarters is a fraction.
Decimals can be termed as a combination of an integral part and a fractional part separated by a decimal point. For example, 2.5 is a decimal where 2 is the integer placed before the decimal point, and 5 is the fractional part after the decimal point.
In simple terms, percent means per hundred. So it is a number expressed as a fraction with a denominator that is 100. Hence percentages are also used to describe parts of a whole number.
So, 10% = \(\frac{10}{100}\)= 0.1
Where 10% is a percent, \(\frac{10}{100}\) is a fraction, and 0.1 is a decimal.
How do we Convert from Percent to Decimal?
As we know, percent means “per 100” so 40% would mean 40 per 100, or we can write it as \(\frac{40}{100}\) . If we divide 40 by 100, we will get 0.4, which is a decimal. We remove the “%” symbol, then divide the number by 100. The quotient on dividing by 100 is the same as the dividend but the decimal point in the quotient has to be moved by two places to the left from its position.
How do we Convert from Decimal to Percent?
As we know, percent means “per 100”, so we multiply the decimal number by 100% to get the percentage value. This is because 100% equals to 1, and multiplying by 1 does not change the value.
An easy way to multiply by 100 for a decimal to turn into percent is by moving the decimal point of the number by 2 places to the right.
Solved Examples
Example 1. Write \(\frac{3}{5}\) as a decimal and a percent.
Solution:
To convert a fraction into a decimal and percent, the denominator of the fraction should be 100. So for \(\frac{3}{5}\) we multiply the numerator and denominator by 20.
\(\frac{3 ~ × ~ 20}{5 ~× ~ 20}\) = \(\frac{60}{100}\)
\(\frac{60}{100}\) = 60%
\(\frac{60}{100}\) = 0.6
So, \(\frac{3}{5}\) can be written as 60% as a percent, and 0.6 as a decimal.
Example 2. The following table shows the portion of students who participated in the annual sports competition from each grade. Order the grades according to the portion participation from the least to the greatest.
Grade | Participation |
|---|---|
3 | \(\frac{4}{5}\) |
4 | 70% |
5 | 0.56 |
Solution: Here, we have a combination of fraction, decimal, and percentage. So to compare, we need to express all of them in terms of a common representation, that is in terms of either like fractions, percents or decimals.
Let’s express all these numbers in terms of decimals, so we will need to write \(\frac{4}{5}\) and 70% as decimals.
\(\frac{4}{5}\) = \(\frac{4 ~ × ~ 20}{5 ~ × ~ 20}\) = \(\frac{80}{100}\) = 0.8 (convert to a fraction with denominator 100 and move the decimal point to the left by two places)
70% = \(\frac{70}{100}\) = 0.7 (moving the decimal point to the left by two places)
Now, let us check the values and order the grades from the least to greatest.
0.56 < 0.7 < 0.8
As per the values, grade 5 is the least, followed by grade 4 and grade 3.
Example 3. Order the numbers from the greatest to least.
0.7, 67%, \(\frac{8}{5}\), \(\frac{11}{50}\)
Solution: Let us convert 67%, \(\frac{8}{5}\), and \(\frac{11}{50}\) to decimals and then order them.
67% = \(\frac{67}{100}\) = 0.67 (moving the decimal point to the left by two places)
\(\frac{8}{5}\) = \(\frac{8 ~ × ~ 20}{5 ~ × ~ 20}\) = \(\frac{160}{100}\) = 1.6 (convert to a fraction with denominator 100 and move the decimal point to the left by two places)
\(\frac{11}{50}\) = \(\frac{11 ~ × ~ 2}{50 ~ × ~ 2}\) = \(\frac{22}{100}\) = 0.22 (convert to a fraction with denominator 100 and move the decimal point to the left by two places)
So, now we have 0.7, 0.67, 1.6, and 0.22.
Ordering them from the greatest to the least:
1.6 > 0.7 > 0.67 > 0.22
There are two methods to do the conversion. First, you can use the long division method to divide the fraction, the quotient is then multiplied by 100, add the “%” symbol, and you get the percent value. Second, you express the fraction such that the denominator is 100. Then the numerator value is taken and put the “%” symbol to get the value.
The “%” symbol basically denotes that there is 100 in the denominator. To express a percent as a fraction, simply remove the (%) sign and write that number as a fraction whose denominator is 100. If possible, the fraction can be further reduced to its simplest form.
Fractions that have the same denominator are called like fractions.