Problem 25 - Elementary and Intermediate Algebra

Question

Write decimal notation for each number. $$ \frac{7}{8} $$

Step-by-Step Solution

Answer

The decimal notation for \( \frac{7}{8} \) is 0.875.

Step 1: Understand the problem

The goal is to convert the fraction \(\frac{7}{8}\) to its decimal form.

Step 2: Divide the numerator by the denominator

To convert the fraction to a decimal, divide 7 by 8.

Step 3: Perform the division

Divide 7 by 8 using long division or a calculator. The result is 0.875.

Step 4: Express the result

The decimal notation for the fraction \( \frac{7}{8} \) is 0.875.

Key Concepts

Fraction to Decimal Conversion

Converting a fraction to a decimal is a simple but crucial skill in math. A fraction consists of a numerator and a denominator. To convert a fraction like \(\frac{7}{8}\) to a decimal, you need to divide the numerator (the top number) by the denominator (the bottom number).

The whole idea is to express the fraction in a different form, where the number is shown with a decimal point. Here are the steps you'll follow:

• Identify the numerator and the denominator in the fraction.
• Perform the division of the numerator by the denominator using long division or a calculator.
• The result obtained will be the decimal form of the fraction.

With practice, this conversion will become second nature!

Long Division

When you don't have a calculator handy, long division is your go-to method for converting fractions to decimals. Let's break it down:

Suppose you want to convert \(\frac{7}{8}\) into a decimal. You'll set up the division problem by placing 7 (the numerator) inside the division bracket and 8 (the denominator) outside.

Here's a simple approach:

• Determine how many times 8 fits into 7. It can't, so you'd write a 0. Add a decimal point and a 0, making it 70.
• Now, see how many times 8 fits into 70. It fits 8 times, so write 8 after the decimal point. Subtract 64 (8 * 8) from 70, leaving you with 6.
• Add another 0, making it 60. Determine how many times 8 fits into 60. It fits 7 times. Write 7 next to the 8. Subtract 56 (8 * 7) from 60, leaving you with 4.
• Add another 0 to make it 40. See how many times 8 fits into 40. It fits 5 times. So, write 5. Now subtract 40 (8 * 5) to get a remainder of 0.

So, the fraction \(\frac{7}{8}\) converts to 0.875 using long division.

Numerator and Denominator

Understanding the roles of the numerator and denominator is essential for mastering fractions and their decimal conversions.

Numerator: This is the top part of a fraction. It indicates how many parts of the whole we are considering. In \(\frac{7}{8}\), 7 is the numerator.

Denominator: This is the bottom part of a fraction. It signifies the total number of equal parts the whole is divided into. In \(\frac{7}{8}\), 8 is the denominator.

Together, they tell us we have 7 parts of something that's been divided into 8 equal parts. To convert it to a decimal:

• Recognize that each part is worth \(\frac{1}{8}\).
• Multiply the numerator by the decimal equivalent of one part (\frac{1}{8} is 0.125).
• Thus, \(7 \times 0.125 = 0.875\).

By understanding these components, converting fractions to decimals becomes a breeze!