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Chapter 13: Problem 47

Express each percent as a decimal. $$77 \%$$

Short Answer

Expert verified
77% as a decimal is 0.77.

Step by step solution

01

Understanding Percentages

Percentages are a way of expressing a number as a fraction of 100. The '%' symbol represents 'per centum' or per hundred. So, 77% means 77 per 100.
02

Converting Percent to Decimal

To convert a percentage to a decimal, we remove the percent symbol (%) and divide the number by 100. Mathematically, this is expressed as: \[ 77\% = \frac{77}{100} \]
03

Performing the Division

We now perform the division from Step 2. Divide 77 by 100 to get the decimal.\[ 77 \div 100 = 0.77 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Percentages
Percentages are a useful way to express proportions. The word 'percent' comes from the Latin 'per centum,' meaning 'per hundred.' So when we say 77%, it literally means 77 parts out of 100. If you were to take a pie and cut it into 100 equal slices, 77% of the pie would mean you have 77 of those slices.
Percentages are commonly used in everyday life, like calculating discounts, interest rates, and statistics. They allow us to easily compare different quantities.
  • Percentages represent parts of a whole.
  • They express how much of something exists compared to the total number of parts.
  • The percent sign (%) symbolizes this concept of per hundred.
Decimal Representation
Decimals are another way to express fractions. A decimal is like a simplified fraction where the denominator is a power of 10. In other words, decimals break a number down into tenths, hundredths, thousandths, and so on.
When we convert percentages to decimals, we're modifying the representation of the number, not its value. For example, 77% becomes 0.77 when represented as a decimal. This means the same thing as 77 per 100, just in a different format.
  • Decimals use a base 10 system to simplify numbers.
  • A number in decimal form has no percent symbol and is expressed using a decimal point.
  • To convert percentages to decimals, adjust the format without changing the actual value.
Division by 100
One crucial step in converting a percentage to a decimal is dividing by 100. This division helps transition from a percentage point to a base 10 decimal form.
The concept is simple: to go from a percentage to a decimal, you remove the percent sign and divide the numeric value by 100, thus repositioning the decimal point. Consider the example:
When you convert 77% to a decimal, you perform the division: \[ 77 \div 100 = 0.77 \]
  • Dividing by 100 shifts the number two places to the left.
  • This step removes the percent character (%) by accounting for the 'per hundred' concept.
  • It's a straightforward yet essential part of decimal conversion.

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