Problem 17 - Elementary Algebra

Question

For exercises \(13-24\), rewrite the fraction as a decimal number. $$ \frac{3}{8} $$

Step-by-Step Solution

Answer

0.375

Step 1 - Understand the Fraction

Examine the fraction \(\frac{3}{8}\). The goal is to convert this fraction into its decimal form.

Step 2 - Division

To convert the fraction to a decimal, divide the numerator (3) by the denominator (8). Set up the long division: 3 divided by 8.

Step 3 - Perform the Division

Perform the long division of 3 divided by 8 which results in 0.375. Here is the calculation: 3.000 divided by 8 equals 0.375.

Step 4 - Write the Decimal

The fraction \(\frac{3}{8}\) is equivalent to the decimal 0.375.

Key Concepts

fraction

Fractions represent parts of a whole. A fraction is composed of a numerator (top number) and a denominator (bottom number). For instance, in the fraction \(\frac{3}{8}\), 3 is the numerator and 8 is the denominator.

Fractions indicate how many parts we have out of a certain total. When you see \( \frac{3}{8} \), it means 3 parts out of 8 total parts. If you cut a pie into 8 equal slices, 3 of those slices make up \( \frac{3}{8} \) of the pie.

One way to grasp fractions is to visualize. Imagine dividing something like an apple or a pizza into equal parts. When you take some parts, you create a fraction.

Fractions can be converted into decimals and percentages, which are alternate representations of the same value.

decimal

Decimals represent fractions in a different form. They use a base-10 system. Whole numbers are to the left of the decimal point, while fractional parts are to the right.

When you convert a fraction like \( \frac{3}{8} \) to a decimal, you're finding a number between whole numbers that signifies the same value. For \( \frac{3}{8} \), the decimal form is 0.375. This breaks it down to a more straightforward form:

• 3 tenths (0.3)
• 7 hundredths (0.07)
• 5 thousandths (0.005)

Decimals are useful because they are easier to add, subtract, multiply, and divide compared to fractions. They are widely used in many areas, such as money, science, and engineering.

long division

Long division is a method used to divide larger numbers. It breaks down a division problem into easier steps. To convert a fraction like \( \frac{3}{8} \) to a decimal, you perform long division where the numerator (3) is divided by the denominator (8).

Here are the steps explained:

• Set up the division: 3 divided by 8.
• Since 3 is smaller than 8, add a decimal point and zeros: 3.000.
• Determine how many times 8 fits into 30. It fits 3 times (because 8 x 3 = 24).
• Subtract 24 from 30, which gives you 6.
• Bring down another zero, making it 60.
• Divide 60 by 8, which fits 7 times (because 8 x 7 = 56).
• Subtract 56 from 60, which gives you 4.
• Bring down another zero, making it 40.
• Divide 40 by 8, which fits 5 times (because 8 x 5 = 40).

From this, you get the decimal 0.375.

Long division helps you understand the process of converting fractions to decimals thoroughly.