Problem 66 - Prealgebra

Question

Write each decimal as an equivalent proper fraction or mixed number. 0.08

Step-by-Step Solution

Answer

0.08 is equivalent to \( \frac{2}{25} \).

Step 1: Understand the Decimal

Recognize that the decimal 0.08 is read as 'eight hundredths'. This indicates it is in the hundredths place in the decimal system.

Step 2: Convert to Fraction

Write 0.08 as a fraction: since it is 'eight hundredths', it can be written as \( \frac{8}{100} \).

Step 3: Simplify the Fraction

Simplify the fraction \( \frac{8}{100} \) by finding the greatest common divisor (GCD) of 8 and 100, which is 4. Divide both the numerator and denominator by their GCD to get \( \frac{2}{25} \).

Step 4: Verify the Fraction

Check your work by converting \( \frac{2}{25} \) back to a decimal. Divide 2 by 25 to ensure it equals 0.08, confirming that \( \frac{2}{25} \) is the correct simplified fraction.

Key Concepts

Simplifying Fractions

Simplifying fractions is like tidying up a math problem. When you have a fraction like \( \frac{8}{100} \), it's essential to reduce it to its simplest form for clarity and ease.

• Begin by identifying a number that can divide both the numerator and the denominator evenly. This is known as the Greatest Common Divisor (GCD).
• In the given example of \( \frac{8}{100} \), the GCD is 4.
• Divide both the numerator and the denominator by the GCD: \( \frac{8 \div 4}{100 \div 4} = \frac{2}{25} \).

Simplified fractions are easier to understand and work with, making math problems less cumbersome. This technique is beneficial when solving equations or converting between fractions and decimals.

Understanding Decimals

Decimals are another way of expressing fractions that stem from the base-10 system. When you see a decimal like 0.08, it might look tricky, but it's quite simple once understood. Let's break it down:

• The decimal 0.08 has two digits after the point, meaning it represents hundredths.
• The number itself, read aloud, is 'zero point zero eight' or 'eight hundredths'.
• This shows it as the fraction \( \frac{8}{100} \).

Understanding how decimals associate with fractions can help ease transitions between different numerical formats. It's like having two different ways to say the same thing. Knowing that decimals and fractions are closely linked provides a significant advantage in mathematics.

Greatest Common Divisor

The Greatest Common Divisor (GCD) is crucial in simplifying fractions like \( \frac{8}{100} \). The GCD is the largest number that can exactly divide both the numerator and the denominator without leaving a remainder.

• To find the GCD of two numbers, list their factors: for 8, the factors are 1, 2, 4, 8; for 100, they are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
• Identify the largest common factor. In this case, it is 4.
• Use this GCD to simplify the fraction: divide both the numerator and denominator by 4 to get \( \frac{2}{25} \).

Finding the GCD ensures that a fraction is reduced to its simplest form. It's a handy tool in math, especially when dealing with large numbers or equations.