Problem 14 - Elementary Algebra

Question

For exercises \(13-24\), rewrite the fraction as a decimal number. $$ \frac{3}{5} $$

Step-by-Step Solution

Answer

0.6

Step 1: Understand the Fraction

The given fraction is \( \frac{3}{5} \). This means 3 divided by 5.

Step 2: Divide the Numerator by the Denominator

To convert the fraction to a decimal, divide 3 by 5. This can be done by performing the division \(3 \, \div \, 5\).

Step 3: Perform the Division

When dividing 3 by 5, the result is 0.6 because 5 goes into 3 zero times, but 5 goes into 30 six times. Therefore, \( \frac{3}{5} = 0.6 \).

Step 4: Write the Answer

Express the final result as a decimal number: 0.6.

Key Concepts

Numerator and Denominator

A fraction comprises two main parts: the numerator and the denominator.
The numerator is the top number, representing the number of parts we have. In this exercise, the numerator is 3.
The denominator is the bottom number, representing the number of equal parts the whole is divided into. Here, it is 5.
Understanding this helps in visualizing and performing operations with fractions. When converting a fraction to a decimal, we need to divide the numerator (top number) by the denominator (bottom number).

Long Division

Long division is a method used to divide large numbers. It consists of dividing the dividend (the number being divided) by the divisor (the number by which we are dividing).
Here, we need to divide 3 (numerator) by 5 (denominator) using long division.
Since 3 is smaller than 5, we notice that 5 cannot go into 3 without producing a decimal or fraction. We add a decimal to 3, making it 3.0 or 30 tenths, and place a decimal point in the result.
We then ask how many times 5 can go into 30, which is 6 times, leading us to the decimal 0.6 after the division.

Decimal Conversion

Decimal conversion of a fraction involves performing the division of the numerator by the denominator.
To convert \( \frac{3}{5} \) into a decimal, we divide 3 by 5.
Using long division, 5 goes into 3 zero times, but 5 goes into 30 (3.0) six times.
Thus, the result of the division is 0.6.
Fractions can always be converted into decimals by this division process, making it easier to understand and compare numerical values. In conclusion, \( \frac{3}{5} = 0.6 \) in decimal form.