Problem 49 - Prealgebra

Question

Convert the given decimal to a mixed fraction. Do not simplify your answer. 414.939

Step-by-Step Solution

Answer

414.939 as a mixed fraction is \( 414 \frac{939}{1000} \).

Step 1: Identify the Whole Number

Look at the decimal number given: 414.939. Identify the whole number part before the decimal point, which is 414. This will be the whole number part of our mixed fraction.

Step 2: Separate the Decimal Part

The decimal part of 414.939 is 0.939. This part of the number needs to be converted into a fraction.

Step 3: Express Decimal as a Fraction

To convert 0.939 to a fraction, recognize that 0.939 can be expressed as \( \frac{939}{1000} \), because 939 is the number after the decimal, and it is over 1000, which represents the thousandths place.

Step 4: Form the Mixed Fraction

Combine the whole number and the fractional part to form the mixed fraction. The number 414.939 as a mixed fraction is \( 414 \frac{939}{1000} \).

Key Concepts

Decimal to Fraction Conversion

Decimals and fractions are two ways of representing numbers that are not whole. Converting a decimal to a fraction is a process that helps you express this number in a fraction form.
Imagine you have a decimal like 0.939, as seen in the exercise. The first step is to look at the number after the decimal point. Here, it's 939. To convert 0.939 to a fraction, think of it as "nine hundred thirty-nine thousandths." This means you express it over 1000, as there are three digits after the decimal. So, 0.939 becomes \( \frac{939}{1000} \).

Remember, the denominator (bottom number) is 1000 because that's the place value farthest after the decimal. More generally:

• One digit after the decimal = tenths = \( \frac{1}{10} \)
• Two digits = hundredths = \( \frac{1}{100} \)
• Three digits = thousandths = \( \frac{1}{1000} \)

Understanding this method allows you to easily convert any decimal to a fraction!

Whole Numbers

Whole numbers are the numbers we count with, starting from zero upwards (0, 1, 2, 3, ...). When dealing with mixed fractions, whole numbers play a crucial role.
In the exercise, the decimal 414.939 has a whole number part, 414. This number is directly in front of the decimal. It remains unchanged in the fraction conversion process and becomes the whole part of a mixed fraction.

Remember:

• A mixed fraction is a combination of a whole number and a proper fraction.
• The whole number is the part of the decimal before the dot.
• You don't modify this part when forming the mixed fraction.

In our example, 414 is taken as it is and will be used directly to form \( 414 \frac{939}{1000} \). Whole numbers in decimals are straightforward – they simply carry over when converting to mixed fractions!

Fractions

Fractions represent parts of a whole. They consist of a numerator and a denominator. In mixed fractions, you combine the concept of whole numbers with fractions.
To form a mixed fraction, you take a whole number and a fraction, as shown in \( 414 \frac{939}{1000} \). The fraction \( \frac{939}{1000} \) represents the decimal portion of the number.

Important points about fractions include:

• The numerator (939, in this case) is the part above the fraction line.
• The denominator (1000) is below the line, indicating into how many equal parts the whole is divided.
• Fractions can often be simplified, but in this exercise, you should not. Simplification means finding an equivalent fraction that is easier to read, like turning \( \frac{4}{8} \) into \( \frac{1}{2} \).

Fractions bring decimal numbers into whole terms, making it easier to work with them in mathematical operations and real-world measurements!