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Chapter 6: Problem 34

In the following exercises, convert each percent to a decimal. $$125 \%$$

Short Answer

Expert verified
125% as a decimal is 1.25.

Step by step solution

01

- Understand the Percent Sign

The percent sign (%) implies 'per hundred'. To convert a percentage to a decimal, the percentage must be divided by 100.
02

- Divide by 100

To convert 125% into a decimal, divide 125 by 100. This can be written as: \[ \frac{125}{100} \]
03

- Simplify the Division

Perform the division: \[ \frac{125}{100} = 1.25 \]

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Key Concepts

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

percent to decimal conversion
Converting a percentage to a decimal might sound tricky, but it's actually quite simple. The percentage sign (%) means 'per hundred'. So, whenever you see a percentage, it's just a number out of 100. For example, 125% means 125 out of 100. Now, to convert this to a decimal, you need to divide the percentage by 100 to see how many parts it represents in a whole number. Hence, 125 becomes 1.25 when converted to a decimal.
dividing by 100
Dividing by 100 is a crucial step when converting percentages to decimals. When you have a percentage, you simply divide it by 100. Let's break it down further:
First, write the percentage as a fraction. For example, 125% becomes \[ \frac{125}{100} \]
Performing this division gives you the decimal form. So, \[ \frac{125}{100} = 1.25 \]
Dividing by 100 simply shifts the decimal point two places to the left. This means that for any percentage, just move the decimal point two spots to the left to get the decimal form.
simplifying fractions
Simplifying fractions is another important mathematical concept. In the context of converting a percentage to a decimal, it's straightforward as you're often working with base numbers like 100. However, understanding simplification is helpful for more complex fractions:
In our example, we had \[ \frac{125}{100} \] which simplifies to 1.25 because dividing both the numerator (125) and the denominator (100) by 100 reduces the fraction. Simplifying fractions means making a fraction as simple as possible so the numerator and the denominator have no common factors other than 1. This makes calculations easier and results clearer.

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Most popular questions from this chapter

In the following exercises, solve. Last year Bernard bought a new car for \(\$ 30,000\) . This year the car is worth \(\$ 24,000\) . Find the percent decrease.

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