Problem 75 Convert each percent to a decima... [FREE SOLUTION]

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Chapter 2: Problem 75

Convert each percent to a decimal. $$ 53 \% $$

Short Answer

Expert verified

0.53

Step by step solution

Understand the Definition of Percent

Percent means 'per hundred.' Therefore, 53% means 53 out of every 100.

Convert Percent to Fraction

Convert 53% to a fraction by writing it as \ \ \ $ \ \frac{53}{100} \ $.

Convert Fraction to Decimal

To convert the fraction \ \ \ $ \ \frac{53}{100} \ $ to a decimal, simply divide the numerator (53) by the denominator (100). This gives \ 0.53 \.

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Key Concepts

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

percent definition

A percent represents a ratio out of 100. It is often used to describe proportions or ratios in various contexts, such as statistics, finance, and general measurements. The symbol for percent is $\%$. For example, 53% means 53 out of every 100. This can be visualized as taking something, like a pie chart, and dividing it into 100 equal parts where 53 of those parts are a certain category or value. Remembering that percent literally means 'per hundred' helps in understanding how to convert between percentages and other forms of representation like fractions and decimals.

fraction conversion

Converting a percent to a fraction is straightforward. You start by writing the percent as a fraction over 100. For instance, 53% becomes\[ \frac{53}{100} \]. A fraction represents the same idea as a percent but in a different form. This fraction can sometimes be simplified depending on the number. In our example with 53%, the fraction\[ \frac{53}{100} \]is already in its simplest form because 53 and 100 have no common factors other than 1. Simplifying fractions generally involves dividing both the numerator and the denominator by their greatest common divisor (GCD).

decimal conversion

Converting a fraction to a decimal involves performing the division indicated by the fraction. For\[ \frac{53}{100} \], you divide 53 by 100, which results in 0.53. Here is a quick way to do this: since the fraction's denominator is 100, you can move the decimal point in the numerator (53) two places to the left. This is equivalent to dividing by 100. Therefore, 53% becomes 0.53 in decimal form. This method works efficiently for any percent where the denominator is a power of 10, like 10, 100, or 1000.

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91影视

Convert each percent to a decimal. $$ 53 \% $$

Short Answer

Step by step solution

Understand the Definition of Percent

Convert Percent to Fraction

Convert Fraction to Decimal

Key Concepts

percent definition

fraction conversion

decimal conversion

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