Problem 275 - Intermediate Algebra

Question

In the following exercises, write each decimal as a fraction. $$ 0.04 $$

Step-by-Step Solution

Answer

0.04 as a fraction is \( \frac{1}{25} \).

Step 1: Identify the decimal place

Notice that the decimal 0.04 is in the hundredths place.

Step 2: Write as a fraction

Since the decimal 0.04 is in the hundredths place, it can be written as the fraction \( \frac{4}{100} \).

Step 3: Simplify the fraction

Simplify the fraction \( \frac{4}{100} \) by dividing the numerator and the denominator by their greatest common divisor, which is 4. This gives \( \frac{4 \times 1}{100 \times 1} = \frac{1}{25} \).

Key Concepts

decimal place

When converting a decimal to a fraction, the first step is to identify the decimal place. This means recognizing which position the digits occupy after the decimal point. For instance, in the number 0.04, the digit 4 is in the hundredths place.
If the decimal was 0.4, the 4 would be in the tenths place. Each position has a specific name:

• Tenths place: 0.1
• Hundredths place: 0.01
• Thousandths place: 0.001

Understanding the decimal place helps in correctly converting the decimal to a fraction.

writing fractions

Once you've identified the decimal place, the next step is to write the decimal as a fraction. The position of the digit tells you the denominator of the fraction. For example, since 0.04 has a digit in the hundredths place, it translates to the fraction \( \frac{4}{100} \). This means 4 out of 100 parts. Here's a useful list to remember:

• 0.1 = \( \frac{1}{10} \)
• 0.01 = \( \frac{1}{100} \)
• 0.001 = \( \frac{1}{1000} \)

So when you see 0.04, you can think of it as \( \frac{4}{100} \). It’s important to place the correct number of zeros in the denominator.

simplifying fractions

After writing the decimal as a fraction, the final step is to simplify it. Simplifying a fraction means making it into its simplest form by dividing both the numerator and the denominator by their greatest common divisor (GCD).
In our example, we have the fraction \( \frac{4}{100} \). The GCD of 4 and 100 is 4. We simplify it by dividing both the numerator and the denominator by 4:
\( \frac{4 \div 4}{100 \div 4} = \frac{1}{25} \).
Simplifying fractions makes them easier to read and work with.