Percent and Decimals Relation Formula
A decimal number is a type of number which has a whole number and the fractional part separated by a decimal point. The word ‘decimal’ originated from the Latin word ‘decimus’, which means ‘tenth’. On the other hand, the word ‘percent’ is derived from the Latin phrase “per centum”, which means “by the hundred”. We use decimal numbers to accurately express quantities like amount of money, the weight of an object, the length of an object and so on. Whereas we use percent to express statistical quantities like scores, growth, profits, losses, discounts and other statistics related to demographics and economics.
Decimal numbers are based on the base-10 number system, which has 10 digits. Since percentages are fractions having 100 (a multiple of 10) as the denominator, decimals are closely related to percentages. Percentages are basically fractions presented in an alternate way which is easier to use. Since decimals and fractions are basically the same, we can say that percentages, decimals and fractions can be used interchangeably. 
It is important to learn the steps involved in the conversion of a percent to a decimal and vice versa. The conversion between decimals and percentages can be carried out either by using simple formulas or by understanding the relationship between decimals and percentages. First, we will learn how to convert decimals and percentages using the formula. Later, we will learn how to perform the conversion by understanding the relationship between them.
List of Formulas
There are two formulas that are associated with percentages and decimal numbers. The first formula is used to convert a decimal number into a percentage, and the second formula is used to convert a percentage into a decimal number.
- Decimal to percent formula
\(Percent=Decimal\times 100\)
- Percent to decimal formula
\(Decimal=Percent\div 100\)
As the name suggests, a percentage is a fraction having 100 as the denominator. So, we need to multiply the percentage value by 100 to remove the 100 in the denominator and find the decimal value. And as you can see, the second formula is the inverse of the first formula. We need to divide a decimal number by 100 to find the percentage value.
Rapid Recall
We have discussed the formulas used to convert a decimal into a percent. Now we learn how to perform the same conversion by understanding the relationship between decimal numbers and percentages. In this method, we need not follow any steps or perform any calculations. We can find the result directly from the provided number.
To convert a percentage value into a decimal number, we can remove the % symbol and move the decimal point two places to the left.
To convert a decimal number into a percentage value, move the decimal point two places towards the right. Then add the % symbol.
Solved Examples
Example 1: Convert 0.21 into percent.
Solution: We can use the following formula to convert a decimal into a percent.
Percent = Decimal × 100
Here, the decimal number is 0.21.
Hence, Percent = 0.21 × 100
= 21%
Therefore, 0.21 = 21%
Example 2: Convert 85% into a decimal number.
Solution: We can use the following formula to convert a percent into a decimal.
Decimal = Percent ÷ 100
Here, the percentage value is 85%.
Hence, Decimal \(=\frac{85}{100}=0.85\)
Therefore, 85% = 0.85
Example 3: Express 1.34 as a percent value.
Solution:
\(Percent=Decimal\times 100\)
Here, the decimal number is 1.34.
So, Percent = 1.34 × 100
= 134%
Hence, 1.34 = 134%
Example 4: Charlie ate 5% of a chocolate bar and Augustine ate 55% of the same chocolate bar. Find the quantity of the chocolate bar that is remaining, in decimal form.
Solution:
Percentage of the chocolate bar that Charlie ate = 5%
Percentage of the chocolate bar that Augustine ate = 55%
Total percentage of the chocolate bar that was consumed = 5% + 55% = 60%
Total percentage of the chocolate bar that is remaining = 100% – 60% = 40%
Now, we need to convert 40% into a decimal number.
Decimal = Percent ÷ 100
= \(\frac{40}{100}\)
= 0.4
Therefore, 0.4 portions of the chocolate are remaining.
Example 5: Shop A sells a computer for 80% of the original price, and shop B sells the same computer for 0.85 times the original price. Which shop sells the computer for a lower price?
Solution:
The price at which shop A sells the computer = 80% of the original price.
The price at which shop B sells the computer = 0.85 times the original price.
We need to convert either the decimal to fraction or the fraction to decimal to compare these values. Here we will convert the decimal into a percent.
Percent = Decimal × 100
= 0.85 × 100
= 85%
So, shop B sells the computer for 85% of the original price. That means shop A sells it for a cheaper price.
The word cent denotes 100. So “percent” means “for every hundred”. A cent is also \(\frac{1}{100}{th}\) of a dollar.
We use percentages to express the comparison between two values easily. It lets us easily express “how much” or “how many” of a quantity is taken from a given value.
A percentage refers to a general relationship rather than a specific measure like percent. “Percent” means “per hundred” and can be written or expressed with the percent symbol “%”.
To convert a percent to a decimal, remove the % symbol and move the decimal point two places to the left. To convert a decimal into a percent, we must move the decimal point two places towards the right and add the % symbol.