Problem 21 - Elementary Algebra

Question

For the following problems, convert each decimal fraction to a fraction. 0.06

Step-by-Step Solution

Answer

Question: Convert the decimal fraction 0.06 into a fraction form. Answer: \(\frac{3}{50}\)

Step 1: Identify the place value of the decimal fraction

The decimal fraction 0.06 has two decimal places. The second digit after the decimal point is in the hundredths place, so 0.06 can be read as "six hundredths."

Step 2: Write the decimal fraction as a fraction

To convert 0.06 to a fraction, we can write it as the ratio of the decimal (6) to the place value (100): \[\frac{6}{100}\]

Step 3: Simplify the fraction

Now, let's see if we can simplify the fraction further. 6 and 100 have a common factor of 2, so we'll divide both the numerator and the denominator by 2: \[\frac{6\div2}{100\div2} = \frac{3}{50}\]

Step 4: Final Answer

The decimal fraction 0.06 can be converted into the fraction form \[\boxed{\frac{3}{50}}.\]

Key Concepts

Decimal Fraction

When you encounter numbers like 0.06, you're dealing with what's known as a decimal fraction. Decimal fractions represent a part of a whole number by using a decimal point. To understand and work with these numbers efficiently, you'll want to be comfortable with both their expression as decimals and their conversion to simple fractions.

Converting a decimal to a fraction involves identifying the place value of the last digit in the decimal and using that as the denominator for your fraction. The number after the decimal point is your numerator. In practical terms, if you have the decimal 0.06, the '6' is in the hundredths place—implying that the denominator will be 100. Thus, the fraction equivalent is written as \(\frac{6}{100}\).

Simplify Fractions

After converting a decimal to a fraction, we often need to simplify the fraction to its lowest terms. Simplifying makes the number easier to understand and work with. To simplify a fraction, you need to find the greatest common divisor (GCD) of both the numerator and the denominator, then divide both by the GCD.

In our example with the fraction \(\frac{6}{100}\), both 6 and 100 can be divided by 2. Doing this reduces the fraction to \(\frac{3}{50}\), which is the simplified form. Remember, the goal here is to make the fraction as simple as possible while ensuring it still holds the same value.

Place Value

Place value is critical when working with any numerical system, particularly with decimals. It helps us recognize the value of each digit in a number based on its position. In a decimal, each place represents a power of 10, moving from left to right after the decimal point.

The first digit to the right of the decimal point is in the 'tenths' place, the second is in the 'hundredths' place, and so on. In the decimal 0.06, the '0' is in the tenths place, and the '6' is in the hundredths place. Consequently, we say the '6' stands for 'six hundredths', which is why the fraction form of 0.06 is initially written as \(\frac{6}{100}\), representing 6 parts out of 100.