Problem 70 - Prealgebra

Question

Write each fraction or mixed number as a decimal. \(\frac{9}{10}\)

Step-by-Step Solution

Answer

The fraction \( \frac{9}{10} \) as a decimal is 0.9.

Step 1: Understand the Fraction

We begin with the fraction \( \frac{9}{10} \). This fraction is read as "nine-tenths," which indicates that 9 is divided by 10.

Step 2: Set Up the Division

To convert the fraction to a decimal, you need to divide the numerator by the denominator. So, set up the division: 9 divided by 10.

Step 3: Perform the Division

When you divide 9 by 10, you move the decimal point one place to the left because dividing by 10 reduces the number by one decimal place. Thus, \( 9 \div 10 = 0.9 \).

Step 4: Write the Decimal

Write the result from your division as a decimal. Therefore, \( \frac{9}{10} \) is written as 0.9 in decimal form.

Key Concepts

Understanding Fractions

Fractions are mathematical expressions used to represent parts of a whole or a division of numbers. A fraction consists of a numerator and a denominator. The numerator indicates the number of equal parts being considered, while the denominator indicates the total number of equal parts in a whole. For example, in the fraction \( \frac{9}{10} \), 9 is the numerator, and 10 is the denominator.
Fractions can represent values less than, greater than, or equal to one.

• When the numerator is less than the denominator, it's a proper fraction, like \( \frac{1}{2} \).
• If the numerator is greater than the denominator, it's an improper fraction, such as \( \frac{5}{3} \).

Converting fractions to decimals can make them easier to understand and compare. It involves dividing the numerator by the denominator.

Exploring Mixed Numbers

Mixed numbers combine whole numbers and fractions to express a quantity. They are useful for clearly showing parts greater than one. In a mixed number, the whole number is written to the left of the fraction. Therefore, a number like 2 \( \frac{3}{4} \) means you have 2 whole units and three-quarters of another unit.
To convert a mixed number into a decimal, follow these steps:

• Convert the fractional part to a decimal using division.
• Add the whole number part to the decimal result of the fraction.

This method allows you to represent numbers accurately while maintaining their value and size.

The Division Process for Decimal Conversion

The division process is crucial in converting fractions and mixed numbers into decimals. It involves dividing the numerator by the denominator to find the decimal equivalent. For example, when converting \( \frac{9}{10} \) to a decimal, you perform the following steps:

• Divide 9 by 10, as the numerator (9) is divided by the denominator (10).
• The division results in moving the decimal point one place to the left since you're dividing by 10. This gives 0.9.
• Thus, the decimal representation of \( \frac{9}{10} \) is 0.9.

When dealing with divisions that do not end quickly, remember that the decimal may repeat or terminate. Understanding this process helps ensure accuracy when converting fractions to decimals.