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Chapter 7: Problem 58

Convert the given fraction to a percent. $$ \frac{3}{2} $$

Short Answer

Expert verified
The fraction \( \frac{3}{2} \) is 150%.

Step by step solution

01

Convert Fraction to Decimal

To convert the fraction \( \frac{3}{2} \) into a decimal, divide the numerator (3) by the denominator (2). This gives: \( 3 \div 2 = 1.5 \).
02

Convert Decimal to Percent

To convert the decimal 1.5 to a percent, multiply by 100. \( 1.5 \times 100 = 150 \).
03

Final Result

The fraction \( \frac{3}{2} \) is equivalent to 150 percent.

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Key Concepts

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

Percent Conversion
When dealing with fractions, converting them into a percent can make it easier to understand their value. Percent means "per hundred," so converting a number to a percent expresses it as a portion of 100. To convert a fraction to a percent:
  • First, convert the fraction into a decimal. This can be done by dividing the numerator by the denominator.
  • Once in decimal form, multiply the result by 100 to convert it to a percentage.
For example, taking the fraction \( \frac{3}{2} \), we divide 3 by 2 to get 1.5. Then, multiplying 1.5 by 100 gives us 150 percent.Converting to a percent helps with understanding comparisons, because it represents how many parts out of 100 the fraction covers.
Decimals
Decimals are a way of representing fractions in a format that is easier to understand and work with mathematically. A decimal point separates the whole number from the fractional part. When converting a fraction to a decimal, as we did with \( \frac{3}{2} \):
  • Divide the numerator (top number) by the denominator (bottom number).
  • The result is the decimal equivalent of the fraction.
For \( \frac{3}{2} \), dividing 3 by 2 gives 1.5.Decimals fit neatly into our number system, making them crucial for various calculations such as adding, subtracting, or converting to percentages.
Numerator and Denominator
Understanding fractions begins with knowing the roles of the numerator and denominator. In any fraction, such as \( \frac{3}{2} \):
  • **Numerator**: The top number (3 in \( \frac{3}{2} \)) indicates how many parts we have.
  • **Denominator**: The bottom number (2 in \( \frac{3}{2} \)) shows into how many equal parts the whole is divided.
When the numerator is larger than the denominator, as in \( \frac{3}{2} \), it results in an improper fraction that exceeds the whole.Knowing how these two parts interact is essential, especially when dividing them to convert into decimals or when comparing different fractions.

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Most popular questions from this chapter

Convert the given decimal to a percent. $$ 0.044 $$

Convert the given percent to a decimal. $$ 28 \% $$

A car rack is marked at $$\$ 405 .$$ However, a sign in the shop indicates that the car rack is being discounted at \(17.5 \%\). What will be the new selling price of the car rack? Round your answer to the nearest penny.

Convert the given fraction to a percent. $$ \frac{9}{2} $$

Convert the given percent to a fraction, and simplify the result. $$ 4 \frac{9}{10} \% $$
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