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Chapter 1: Problem 637

Convert each percent to a decimal. $$ 7.8 \% $$

Short Answer

Expert verified
0.078

Step by step solution

01

Understand the Conversion Rule

To convert a percentage to a decimal, divide the percentage by 100. This is because the term 'percent' means per hundred.
02

Perform the Division

Divide 7.8 by 100. Mathematically, this is represented as 7.8 梅 100.
03

Simplify the Result

Perform the division to get the decimal form. i.e., 7.8 梅 100 = 0.078.

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Key Concepts

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

conversion rules
Understanding how to convert percentages to decimals is a key concept in math. The rule is quite simple: to convert any percentage to a decimal, you divide the percentage by 100. This is because the term 'percent' literally means 'per hundred'. Think of it this way: when you see a percentage, you're seeing a number out of 100.
For example:
  • 20% means 20 out of 100, or 20/100 in fraction form.
  • 50% means 50 out of 100, or 50/100 in fraction form.

By dividing by 100, you're essentially converting the percentage to a fraction of 1, which is the decimal form. Always remember this simple rule: percentage 梅 100 = decimal.
division by 100
When converting percentages to decimals, the step involving division by 100 can be very straightforward, but it helps to understand the mechanics behind it.
Division by 100 shifts the decimal point two places to the left. For instance, moving the decimal point for 7.8%:
  • 7.8% has an implicit decimal point between 7 and 8, i.e., 7.8.
  • Dividing by 100 shifts the decimal two places to the left:
  • First shift: 0.78
  • Second shift: 0.078

As seen, moving the decimal two places left turns 7.8% into 0.078. Remember, regardless of how large or small the percentage, the rule holds: shift the decimal left by two places.
decimal representation
Once you convert a percentage to its decimal form, it's important to understand what the resulting decimal represents.
Consider the decimal form of 7.8% (0.078). This means that for every 1 unit, 7.8% of it is equivalent to 0.078 in decimal form.
Here are some important aspects:
  • Decimals are part of the base-10 number system. They represent fractions of ten, hundreds, thousands, etc.
  • Converting percentages to decimals simplifies arithmetic operations like multiplication and division since working with fractions out of 1 (decimals) is often simpler.

In the bigger picture, understanding decimal representation helps in various real-world applications such as calculating discounts, interest rates, and statistical data.

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Most popular questions from this chapter

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