Percentage, Conversion of Percentage

Percentage, Conversion of Percentage

What is a Percentage?

Percent means “for every 100” or "out of 100." The (%) symbol as a quick way to write a fraction with a denominator of 100. As an example, instead of saying "it rained 14 days out of every 100," we say "it rained 14% of the time."
Percentages can be written as decimals by moving the decimal point two places to the left:

Decimals can be written as a percentages by moving the decimal point two places to the right:

Conversions

Fraction to Percent

The easiest way to convert from a fraction to a percent is to divide the numerator by the denominator and then multiply by 100.
For example, 5/8 = (5 ÷ 8) x 100 = 62.5

Decimal to Percent

To convert a decimal to a percent, multiply by 100.
For example, 0.45 = (0.45) x 100 = 45%

Percent to Fraction

Percent can be thought of as a ratio with a base of 100. Ratios can be written as fractions. So to convert a percent to a fraction we make the numerator on the top the percent value and make the denominator at the bottom 100. This fraction can often be simplified as shown in the example below.
For example, 35% = 35/100 = 35÷5/100÷5 = 7/20

Percent to Decimal

A percent is a ratio with a base of 100. So, to change a percent to a decimal, remove the percent symbol and divide by 100.
For example, 35% = 35/100 = 0.35

Percent/ Decimal/ Fraction Conversions to Memorize

Memorizing or at least being able quickly recall the equivalent percents, decimals, and fractions listed below will be of great assistance to students as they tackle problems that require changing between the different types. Quick recall of these will also help in everyday-type-situations such as comparing price discounts. e.g. what's the best deal, one-third off, or 25% off?

 Percent Fraction Decimal 100/3% 1/3 33.33 25% 1/4 0.25 50% 1/2 0.5 75% 3/4 0.75

Percentage and Ratio

We know that ratio means comparing quantities. Suppose there are 8 mangoes and 12 oranges. The ratio of mangoes to oranges will be 8 : 12 = 2 : 3.
Let us compare ratio using percentages.
Since there are total of 20 fruits, so percentage of mangoes = 8/20 × 100 = 40% and percentage of oranges = 12/20 × 100 = 60%

Example: For making golden chain of 22 carats, 4 g of copper is added to 21 g of gold. Find the percentages of gold and copper in the chain.

Solution: Here, gold : copper :: 21 : 4.
Total weight of both the metals = 21 + 4 = 25
So, 21/25 part is gold and 4/25 part is copper.
Thus, the percentage of gold in the chain = 21/25 × 100 = 84% and percentage of copper in the chain = 4/25 × 100 = 16%.

To Find the Percentage of a Given Quantity

To find the percentage of a given quantity, we change the per cent into fraction and multiply it by the given quantity. Let us illustrate it with the help of following example.

Example: Find.
a. 20% of Rs 500                       b. 3.5% of 1400 kg

Solution:
a. 20% of Rs 500 = 20/100 × Rs 500 = Rs 100
b. 3.5% of 1400 kg = 3.5/100 × 1400 kg = 3.5 × 14 kg = 49 kg

To Express One Quantity as a Percentage of the Other

To express one quantity as a percentage of the other quantity, follow these steps:
1. Convert the quantities into the same unit.
2. Express the two quantities into a fraction with the number to be compared as the
numerator and the number with which it is to be compared as the denominator.
3. Multiply the fraction with 100 and express the answer as per cent (%).

When we express one quantity as a percentage of another quantity, then
Percentage = (One quantity/Other quantity) × 100%

Example 1: Express 6 hours as a per cent of a day.

Solution: 6 hours as a per cent of a day = 6 hours/24 hours = ¼ (Since 1 day = 24 hours).
Hence, required per cent = 1/4 × 100% = 25%.

Example 2: What per cent is
a. 25 p of Rs 6.25?                        b. 22 seconds of 7 minutes 20 seconds?

Solution:
a. Rs 6.25 = 625 p
Required percentage = 25/625 × 100% = 4%
b. 7 minutes 20 seconds = (7 × 60 + 20) seconds = 440 seconds
Required percentage = 22/440 × 100% = 5%

Percentage Increase

If the value of an article increases to a new value, then we calculate percentage increase in the value of that article as follows:
Percentage Increase = (Total Increase/Initial Value) × 100%
= (New Value Initial Value)/Initial Value × 100%

Example: The price of a flat increases from Rs 2500000 to Rs 2750000. Calculate the
percentage increase in the price of the flat.

Solution: Initial price of the flat = Rs 2500000 and the new price of the flat = Rs 2750000
Percentage Increase = (New Value Initial Value)/Initial Value × 100%
= (2750000 2500000)/2500000 × 100% = 250000/2500000 × 100% = 10%
Hence, the percentage increase in the price of the flat is 10%.

Percentage Decrease

If the value of an article decreases to a new value, then we calculate percentage decrease in the value of that article as follows:
Percentage decrease = (Total Decrease/Initial Value) × 100%
= (Initial Value New Value)/Initial Value × 100%

Example: The marks of Rajesh decrease from 75 to 60 in Mathematics. Calculate the
percentage decrease in the marks.

Solution: Initial marks = 75 and new marks = 60
Percentage Decrease = (Initial Value New Value)/Initial Value × 100%
= (75 60)/75 × 100% = 15/75 × 100 = 1/5 × 100% = 20%
Hence, the percentage decrease in marks is 20%.

Percentage Error

Percentage error in a quantity can be calculated as follows:
Percentage Error = Error/Original value × 100%

Example: The length of a table was 200 cm but was wrongly recorded as 225 cm. Find the percentage error.

Solution: Error = 225 cm – 200 cm = 25 cm

Thus, percentage error = 25/200 × 100% = 12.5%