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Chapter 7: Problem 8

Write each percent as a decimal. $$ 62 \% $$

Short Answer

Expert verified
62% as a decimal is 0.62.

Step by step solution

01

Understand the Percentage

The percentage represents a part out of 100. So, 62% means 62 out of every 100.
02

Convert the Percentage to a Fraction

Write 62% as a fraction by placing 62 over 100: \( \frac{62}{100} \).
03

Convert the Fraction to a Decimal

To convert \( \frac{62}{100} \) to a decimal, divide the numerator by the denominator: \( 62 \div 100 = 0.62 \).

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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 way to express numbers as parts of a whole. They represent values out of 100. When you hear someone say a percentage, like 50% or 75%, they're talking about how many parts out of 100 something is. It's like slicing a pizza into 100 pieces and saying how many slices are available.
  • The symbol % is used to denote a percentage, for example, 62%.
  • Percentages help in comparing proportions, like determining how much money is spent on groceries each month compared to your overall budget.

Understanding percentages is essential because they are everywhere鈥攆rom discounts during sales to statistics in reports.
Fractions to Decimals
Converting fractions to decimals is a key skill that can simplify and clarify numbers, especially when dealing with percentages. A fraction consists of a numerator (top number) and a denominator (bottom number). The fraction \( \frac{a}{b} \) can be converted into a decimal by dividing \( a \) by \( b \).
  • For example, \( \frac{62}{100} \) turns into 0.62 by performing the division 62 梅 100.
  • This process breaks down the fraction into parts of a whole, expressed in tenths, hundredths, etc.

The conversion from fractions to decimals is especially useful for visualizing and calculating percentages in real-world scenarios.
Basic Arithmetic and Division
Basic arithmetic includes fundamental operations like addition, subtraction, multiplication, and division. Understanding these is crucial for solving various math problems.

When converting percentages to decimals, division plays a central role. The operation of dividing is used to transform fractions into decimals, as it tells us how many times the denominator fits into the numerator. In our example, dividing 62 by 100 involves moving the decimal point to the left by two places because you are dividing by a power of 10:
  • Step 1: Start with 62.
  • Step 2: Move the decimal point two places left to account for dividing by 100.
  • Result: 0.62

This straightforward use of division makes complex problems simpler and aids in the effective computation of percentages into decimals.

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