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%
Nice explanation.
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