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Chapter 5: Problem 578

Convert Fractions to Decimals $$ \frac{3}{5} $$

Short Answer

Expert verified
The decimal form of \(\frac{3}{5}\) is 0.6.

Step by step solution

01

Understand the Fraction

We start with the fraction \(\frac{3}{5}\). This consists of a numerator (3) and a denominator (5).
02

Convert to Division

To convert the fraction to a decimal, treat the fraction as a division problem where the numerator is divided by the denominator: 3 梅 5.
03

Perform the Division

Perform the division: 3 梅 5. Since 3 is smaller than 5, we can place a decimal point after 3, making it 3.0 梅 5. Proceed with the division by moving the decimal point up and adding zeroes as needed: \(3.0 \div 5 = 0.6\).
04

Check the Answer

Verify the result by multiplying the decimal form back by the denominator to ensure it equals the numerator: 0.6 x 5 = 3.

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Key Concepts

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

Fractions
A fraction represents a part of a whole. It's written with two numbers separated by a slash. The top number is called the numerator, and it tells us how many parts we have. The bottom number is the denominator, and it tells us into how many equal parts the whole is divided. For example, in the fraction \( \frac{3}{5} \), 3 is the numerator, and 5 is the denominator. This means we have 3 out of 5 equal parts.
Division
To convert a fraction to a decimal, you treat it like a division problem. The fraction \( \frac{3}{5} \) means 3 divided by 5. Here, the numerator (3) is divided by the denominator (5). When performing the division, if the numerator is smaller than the denominator, you will need to add a decimal point and zero to the numerator. For instance, 3 divided by 5 is the same as 3.0 divided by 5, which is 0.6.

It's helpful to remember that division and fractions are closely related. Every fraction is a division problem waiting to be solved.
Decimal Conversion
Converting a fraction to a decimal involves simple division. Here鈥檚 how you do it step-by-step:
  • Write down the fraction \( \frac{3}{5} \) as a division problem: 3 梅 5.
  • Since 3 is smaller than 5, place a decimal point right after the 3, making it 3.0.
  • Divide 3.0 by 5. Perform the division: \( 3.0 \div 5 = 0.6 \).
  • Check your answer by multiplying: \( 0.6 \times 5 = 3 \).
This process shows how you change a fraction into an easy-to-understand decimal format. By converting fractions to decimals, you can often simplify problems and make comparisons more straightforward. Decimals are particularly useful in various real-life applications like money, measurements, and statistics.

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Most popular questions from this chapter

In the following exercises, convert each decimal to a fraction or mixed number. $$9.04$$

Simplify. \(10 \div 0.1+(1.8) 4-(0.3)^{2}\)

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Why is there no real number equal to \(\sqrt{-64} ?\)

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