Problem 74 - Prealgebra

Question

Write each fraction or mixed number as a decimal. \(\frac{7}{8}\)

Step-by-Step Solution

Answer

The decimal form of \( \frac{7}{8} \) is 0.875.

Step 1: Understand the Problem

We need to convert the fraction \( \frac{7}{8} \) into a decimal form. This involves dividing the numerator by the denominator.

Step 2: Set Up the Division

Set up the division of 7 by 8. We can do this either on paper, or using a calculator for simplicity.

Step 3: Start Dividing

Divide 7 by 8. Since 7 is less than 8, the decimal will start with 0 (0 point something). We can write this out as 7.000 divided by 8 to help with the division.

Step 4: Perform the Division

Perform the division: 8 goes into 70 eight times (8 x 8 = 64). Subtract 64 from 70 to get 6. Bring down the next zero to make it 60.

Step 5: Continue the Division

Continue dividing: 8 goes into 60 seven times (8 x 7 = 56). Subtract 56 from 60 to get 4. Bring down the next zero to make it 40.

Step 6: Finish the Division

8 goes into 40 five times (8 x 5 = 40). Subtract, and you're left with 0, meaning the division is complete.

Step 7: Conclude the Answer

The division of 7 by 8 results in the decimal 0.875.

Key Concepts

Division

Division is a core mathematical operation that answers the question of how many times one number is contained within another. When converting a fraction to a decimal, you essentially perform division with the numerator divided by the denominator.

The division process involves several steps:

• Identify the Dividend and Divisor: In our fraction \( \frac{7}{8} \), 7 is the dividend (the number to be divided), and 8 is the divisor (the number by which you divide).
• Divide the Numbers: You align the division so that the numerator (7) is inside the division bracket, and the denominator (8) is outside. Since 7 is less than 8, the division will include a decimal.
• Add Decimal Precision: To find the decimal, you add zeros to the dividend, turning it into 7.000. This helps in achieving a more accurate decimal.

The division continues until there are no remainder or the decimal pattern repeats. Understanding division is critical for tasks like converting fractions to decimals.

Numerator and Denominator

The terms numerator and denominator are fundamental in fractions. A fraction represents a part of a whole and is expressed as \( \frac{a}{b} \), where:

• Numerator (a): This is the top number of the fraction. It signifies how many parts you have.
• Denominator (b): This is the bottom number. It shows how many equal parts the whole is divided into.

In many math problems, understanding these terms helps clarify operations like addition, subtraction, and especially conversion into decimals.

When converting a fraction like \( \frac{7}{8} \), the numerator is 7 and the denominator is 8. The conversion involves dividing the numerator by the denominator, showing how you can express the fraction as a decimal. Appreciating the role of these components allows one to easily grasp the dynamic of fractions and their conversion processes.

Decimal Representation

Decimal representation is a way to jot down numbers that fall between integers, using the base ten system. Converting fractions to decimals helps in understanding and comparing values in a straightforward manner.

When you convert \( \frac{7}{8} \) through division, you arrive at the decimal 0.875. This decimal shows a clear, linear position between whole numbers on a number line. Decimal numbers use a period (dot) to separate the whole part from the fractional part. In 0.875:

• Whole Number: 0, indicating no whole units.
• Decimal Fraction: 875, left to right, gives increasingly smaller fractional parts: tenths, hundredths, thousandths.

Decimal involvement is crucial not only in math but also in handling everyday tasks like financial calculations and measurements. Recognizing the equivalent decimal form of a fraction often provides clarity and ease in computations and estimations.