Problem 32 - Prealgebra

Question

Write each decimal as a mixed number. $$8.04$$

Step-by-Step Solution

Answer

8.04 as a mixed number is 8 1/25.

Step 1: Identify the Whole Number and Decimal Part

First, break down the decimal into a whole number and a decimal part. In this case, the number is 8.04, where 8 is the whole number and 0.04 is the decimal part.

Step 2: Convert Decimal to Fraction

The decimal part of the number is 0.04. To convert it into a fraction, recognize that 0.04 is equivalent to \( \frac{4}{100} \). Simplify the fraction \( \frac{4}{100} \) by dividing both the numerator and the denominator by 4, which results in \( \frac{1}{25} \).

Step 3: Combine into a Mixed Number

The original number 8.04 is equivalent to combining the whole number and the simplified fraction. Therefore, \( 8.04 = 8 \frac{1}{25} \). This means the mixed number representation of the decimal 8.04 is 8 and \( \frac{1}{25} \).

Key Concepts

Decimal to Fraction

If you're working with a decimal and need to convert it to a fraction, start by understanding the place value of the decimal. Each digit in a decimal number has a specific place value based on its position relative to the decimal point.
For instance, in the decimal 0.04, the digit 4 is in the hundredths place. This means it can be expressed as the fraction \( \frac{4}{100} \).
Remember, the denominator of the fraction depends on the decimal place:

• Tenths place – denominator is 10
• Hundredths place – denominator is 100
• Thousandths place – denominator is 1000, and so forth

Converting the decimal helps in simplifying complex calculations by using fractions.

Simplifying Fractions

Simplifying fractions is an essential math skill that makes working with numbers easier and more efficient. Once you've converted a decimal to a fraction, the next step is usually to simplify it.
To simplify \( \frac{4}{100} \), find the greatest common divisor (GCD) of both the numerator and the denominator.
Both 4 and 100 are divisible by 4, which is the GCD.

• Divide the numerator \(4\) by 4 to get \(1\)
• Divide the denominator \(100\) by 4 to get \(25\)

Hence, \(\frac{4}{100}\) simplifies to \(\frac{1}{25}\).
Simplifying is vital as it makes fractions easier to compare, add, subtract, and use in further calculations.

Mixed Numbers

A mixed number combines a whole number with a fraction. When you convert a decimal to a mixed number, you're essentially splitting the decimal into two components: a whole number and a fraction.
Taking our example of 8.04, the whole number is 8. The fraction, after converting and simplifying 0.04, is \( \frac{1}{25} \).
Thus, the mixed number representation is 8 and \( \frac{1}{25} \).

• The whole number shows how many full units you have.
• The fraction shows an additional part of a unit.

Mixed numbers are useful when you need to understand quantities in terms of both complete parts and portions, such as in measurements or cooking recipes.