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Chapter 6: Problem 33

In the following exercises, convert each percent to a decimal. $$115 \%$$

Short Answer

Expert verified
1.15

Step by step solution

01

Identify the given percent

The given percent is 115%.
02

Understand the percent to decimal conversion

To convert a percent to a decimal, divide the percent value by 100.
03

Perform the division

Divide 115 by 100: \[ 115 \div 100 = 1.15 \]
04

Write the decimal

After dividing 115 by 100, the result is 1.15.

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Key Concepts

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

Percent Conversion
Percent conversion is a common mathematical operation. To start, understand that percent means 'per hundred.' So when you see a number followed by the percent symbol (\(\%\)), it signifies how many parts out of 100 parts. For example, 50\% means 50 parts out of 100, or simply half.
In the exercise, we aim to turn 115\% into a decimal. Every percent can be converted to a decimal. This is crucial for various applications, including finances, statistics, and data analysis.
To convert a percent to a decimal, we will use division, specifically 'division by 100'.
Decimal Notation
Once we've understood our given percent value, the next step is to change its form. We want to switch from a percent to decimal notation. Decimal notation is simply another way of writing numbers. It's used to represent fractions and whole numbers in a format that includes a decimal point.
For example, the fraction \( \frac{1}{2} \) is written in decimal notation as 0.5. Similarly, when we convert 115\% into decimal notation, it will make calculations easier.
We accomplish this conversion by dividing the percent by 100, since percent means 'per hundred.' This means moving the decimal point two places to the left. So, 115\% becomes 1.15.
Division by 100
Division by 100 is the key mathematical operation for percent to decimal conversion. Let's break it down.
To convert 115\% to a decimal, we divide 115 by 100. In mathematical terms, this is written as:
\[ 115 \div 100 = 1.15 \]
This simple division effectively moves the decimal point two places to the left. Imagine shifting the decimal point from the end of 115 to just before the 1, creating 1.15. Every time, whether it's 50\%, 75\%, or 115\%, you always divide by 100.
This makes percent to decimal conversions straightforward and consistent.

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