Problem 104 - Introductory and Intermediate Algebra for College Students 4th

Question

Explain how to express \(\frac{3}{8}\) as a decimal.

Step-by-Step Solution

Answer

The fraction \(\frac{3}{8}\) expressed as a decimal is 0.375

Step 1: Write the fraction as a division problem

The fraction \(\frac{3}{8}\) can be viewed as 3 divided by 8. We can write this as \(3 \div 8\).

Step 2: Apply long division

Take 3 (the numerator) and divide it by 8 (the denominator) using the long division method. As 3 is less than 8 and cannot be divided into equal parts, we add a decimal point to 3 and consider it as 3.0. After adding the decimal point, you can continue the long division process until you've reached a decimal that rounds to a nearby value or perfectly divides.

Step 3: Write down the result

Write down the decimal number you get as the result from the long division.

Key Concepts

Long Division

Long division is a method used to divide larger numbers into smaller parts, often yielding a decimal when there isn't a perfect division. It is an essential skill for converting fractions into decimals. To understand long division, think of it as breaking down a complex division problem into a series of easier steps.
First, you'll set up the division by placing the dividend (the number you are dividing) inside the long division symbol (also known as a bracket or a divisor line) and the divisor (the number you are dividing by) outside.

• In our example, the dividend is 3, and the divisor is 8.
• If the dividend is smaller than the divisor, as it is here, you'll need to add a decimal point to make it divisible.

This process not only helps with converting fractions to decimals but also improves understanding of division as a whole by breaking complex divisions into smaller, manageable parts.

Division Problem

A division problem involves breaking down a number (the dividend) into equal parts defined by another number (the divisor). When expressing fractions as decimals, you set up a division problem where the numerator becomes the dividend and the denominator becomes the divisor.

To illustrate this with \(\frac{3}{8}\):

• The fraction represents the division \(3 \div 8\).
• Since 3 is less than 8, there's no whole number before the decimal point. This is where adding a decimal to make it 3.0 helps.
• Performing the division gives a more digestible form, which in this case is 0.375.

Setting fractions as division problems is the starting point for converting them to decimals. By viewing the fraction as a division, you prepare for the process of determining decimal value through long division.

Fractions as Decimals

Converting fractions to decimals is a common mathematical conversion, often requiring the use of the long division method. A fraction like \(\frac{3}{8}\) is simply a division of 3 by 8. This fraction, when expressed as a decimal, shows how much of the whole number 8 is occupied by 3.

To convert:

• Identify numerator and denominator as dividend and divisor.
• Apply long division to find an accurate decimal.
• Continue dividing until reaching a terminating decimal or a repeating cycle.

In the example given, fraction \(\frac{3}{8}\) converts to the decimal 0.375. Converting fractions into decimals with precision helps in various applications, from everyday measurements to complex mathematical calculations.