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A percent calculator is an online tool that helps us calculate the percent proportion, percent equation, percent change and percent error. Let us familiarize ourselves with the calculator....Read MoreRead Less

**1.1** Percent proportion

**1.2** Percent equation

**1.3** Percent change

**1.4** Percentage error

Percent is a number represented as a fraction with 100 as its denominator and is represented by the symbol “%”.

There are three inputs for these calculators: percent (p), part of the whole (a) and the whole (w). When any two out of the three are known, the third quantity can be calculated.

But, how are p, w and a related?

The basic form of the percent equation is “p percent of w is a.” Algebraically, this is written as:

a = p% × w, which is the percent equation.

\(a=\frac{p}{100}{\times}w\) (% symbol denotes 100 is in the denominator)

\(\frac{a}{w}=\frac{p}{100}{\times}\frac{w}{w}\) (Divide by w, by division property of equality)

\(\frac{a}{w}=\frac{p}{100}\) , this is the percent proportion.

We call it a percent proportion when the ratio of the part to the whole is equal to the ratio of the percent to 100.

Therefore, we can see that the percent proportion and percent equation are the same but expressed differently. Hence the values obtained from both the calculators would be the same, but the process followed is slightly different.

Percent change is the percent by which a number has changed from its original value. To find the percent change, we first find the change in value, that is the difference between the final and original amount. The change in value is divided by the original amount and then multiplied by 100 to get the percent change.

\({\text{Percent change}}=\frac{\text{new amount – original amount}}{\text{original amount}}{\times}100\)

- When the final amount is greater than the original amount, then it is a percent increase.
- When the original amount is greater than the final amount, then it is a percent decrease.

A percent error is the percent by which the observed amount is different from the actual amount. The Error amount, that is, the change in value is divided by the Actual amount and then multiplied by hundred to get the percent error.

\({\text{Percent error}}=\frac{\text{Error amount}}{\text{Actual amount}}{\times}100\)

where, Error amount = Actual amount – Observed amount

- When the actual amount is greater than the observed amount, then we get a positive error amount.
- When the observed amount is greater than the actual amount, then we get a negative error amount.

**Example 1:****What percent of 80 is 20?**

**Solution:**

\(\frac{a}{w}=\frac{p}{100}\) Write the percent proportion

Where ‘a’ is the part of the whole, ‘w’ is the whole (total) amount, and ‘p’ is the percentage.

\(\frac{20}{80}=\frac{p}{100}\) Substitute 20 for a and 80 for w.

\(\frac{20}{80}{\times}100=\frac{p}{100}{\times}100\) Multiplication Property of equality

\(p=100{\times}\frac{20}{80}\) Simplify

p = 25 %

So, 25% of 80 is 20.

**Example 2:****What number is 14% of 350?**

**Solution:**

a = p % × w Write the percent equation

Where ‘a’ is the part of the whole, ‘w’ is the whole (total) amount, and ‘p’ is the percentage.

\(a=\frac{14}{100}{\times}350\) Substitute \(\frac{14}{100}\) for p% and 350 for w.

a = 49 Simplify.

So, 49 is 14% of 350.

**Example 3: ****What is the percent change in the weight of John, if he had increased to 70 kg from 60 kg?**

**Solution:**

Given,

Original amount = 60 kg

New amount = 70 kg

70 > 60, so it is a percent increase

\({\text{Percent change}}=\frac{\text{new amount – original amount}}{\text{original amount}}{\times}100\)

= \(\frac{\text{70 – 60}}{60}{\times}100\)

= 16.66%

Thus, John has increased his weight by 16.66%.

**Example 4:****The school organized a party that was open to the public. It was predicted that 1,000 teachers and students would visit the party. However, the actual number of people who visited the fest was 1050. Calculate the percent error.**

**Solution:**

Given,

Actual amount = 1050

Observed Amount = 1000

Error amount = Actual amount – Observed amount

= 1050 – 1000

= 50

\({\text{Percent error}}=\frac{\text{Error amount}}{\text{Actual amount}}{\times}100\)

= \(\frac{50}{1050}{\times}100\)

= 0.0476 × 100

= 4.76%

Hence, the percent error is 4.76 %.

Frequently Asked Questions

Percentage error is a measure of the accuracy for any test or experiment. This method allows you to determine whether the data collection is progressing correctly or not. It is widely used by mathematicians and corporate professionals. It is also very important for students who want to study economics.

A proportion is the relationship or equality between two ratios or fractions, whereas a percentage is a ratio or fraction with a constant denominator of 100. Fractions can be used to express both proportion and percentage.

Incrementals (or increases) and decreases are the two types of percentage changes, which are used to express the measure of how an initial value has changed to reach the final value.

Percentage change and percentage difference are not equal because in percentage difference we take the average of the given two numbers as the point of reference. While in percentage change point of reference is one of the numbers.

The division property of equality states that when both the sides of the equation are divided by the same non-zero number, then the equation remains the same or equal.

The symbol % basically denotes that there is 100 in the denominator.