Problem 45 - Prealgebra

Question

Convert the given decimal to a mixed fraction. Do not simplify your answer. 915.239

Step-by-Step Solution

Answer

\( 915\frac{239}{1000} \)

Step 1: Separate the Whole Number

The whole number part of the decimal 915.239 is 915. This forms the whole number portion of the mixed fraction.

Step 2: Identify the Decimal Part

The decimal part of the number is 0.239. We will now focus on converting this part into a fraction.

Step 3: Construct the Fraction

The decimal 0.239 is represented as \( \frac{239}{1000} \) because there are three digits in the decimal, making the denominator 1000 (as 239 is in the thousandths place).

Step 4: Form the Mixed Fraction

Combine the whole number with the fraction obtained from the decimal part. So, the mixed fraction is \( 915\frac{239}{1000} \).

Key Concepts

Whole Number Separation

When you begin converting a decimal to a mixed fraction, the first step is to identify and separate the whole number part from the decimal. For instance, in the decimal 915.239, the digits before the decimal point, 915, represent the whole number part. This number remains unchanged throughout the conversion process and forms the whole number portion of the mixed fraction. This separation sets the foundation for the entire conversion process, allowing you to focus separately on turning the decimal component into a fraction.

Constructing Fractions from Decimals

Once the whole number is set apart, the next step involves transforming the decimal part into a fraction. In the example of 915.239, we look at 0.239. To do this, we consider the decimal ".239" on its own. A general method to construct a fraction from a decimal is to use the digits after the decimal point as the numerator, in this case, 239. The denominator is determined by the place value of the decimal, which in this scenario is the thousandths place. Therefore, the fraction becomes \( \frac{239}{1000} \). This fraction combines with the whole number already identified to form the complete mixed fraction.

Place Value in Fractions

An essential concept in creating a fraction from a decimal lies in understanding the place value of the decimal digits. Place value helps dictate the fraction's denominator. For example, in our decimal 0.239, the number goes to the thousandths place. Here's how place value works:

• Tenths place: first digit after the decimal, denominator is 10.
• Hundredths place: second digit after the decimal, denominator is 100.
• Thousandths place: third digit after the decimal, denominator is 1000.

In the decimal 0.239, the 9 is in the thousandths place, which is why the fraction becomes \( \frac{239}{1000} \). Grasping place value is critical, as it allows us to form a fraction accurately reflecting the position and scale of decimals.