Problem 41 - Prealgebra

Question

In Exercises 41-52, convert the given decimal to a mixed fraction. Do not simplify your answer. 98.1

Step-by-Step Solution

Answer

98.1 as a mixed fraction is \( 98 \frac{1}{10} \).

Step 1: Understanding the problem

We need to convert the decimal number 98.1 into a mixed fraction. A mixed fraction consists of a whole number and a fractional part.

Step 2: Identifying the whole number

The whole number part of the decimal is 98 because 98.1 is greater than 98 but less than 99.

Step 3: Converting the fractional part

The decimal part is 0.1. We need to express this as a fraction. Recall that 0.1 is equivalent to 1/10.

Step 4: Formulating the mixed fraction

Combine the whole number 98 with the fractional part 1/10 to form the mixed fraction. Therefore, 98.1 as a mixed fraction is \( 98 \frac{1}{10} \).

Key Concepts

Decimal to Mixed Fraction Conversion

Converting a decimal to a mixed fraction is a useful skill, especially when dealing with numbers that have both a whole and a fractional part. A decimal such as 98.1 contains a whole part (98) and a fractional part (0.1). The process of conversion involves separating the two parts and expressing them as a mixed fraction.

Start by identifying the whole number in the decimal. This is straightforward; it's everything before the decimal point. For 98.1, the whole part is 98. Once you have this, your next step is to look at the digits following the decimal point. The digits represent the fractional part. In our example, that's 0.1.

To convert the fractional part into a fraction, focus on place value. Here, 0.1 is in the tenths place, which means it equates to 1/10. Finally, you combine both parts—the whole number and the fraction—to form a mixed fraction. Thus, 98.1 converts to the mixed fraction \( 98 \frac{1}{10} \).

Mixed Fractions

A mixed fraction is a combination of a whole number and a fractional part. It's commonly used in everyday math situations when you need to express numbers that aren't whole. Think of recipes, measurements, or when dividing items unevenly!

A mixed fraction follows the format of a whole number next to a fraction, such as \( 2 \frac{3}{4} \). Here, 2 is the whole part and \( \frac{3}{4} \) is the fractional part. Together, they represent a value between two whole numbers—in this case, something greater than 2 but less than 3.

Mixed fractions are practical because they clearly show how much more than the whole is present. They're also easier to understand when visualizing quantities, compared to improper fractions, which combine both components into a single fraction greater than one. Mixed fractions simplify the understanding of parts in relation to whole amounts.

Fractional Parts in Decimals

The fractional part of a decimal is the portion that comes after the decimal point. For example, in the number 98.1, the ".1" is the fractional part. Understanding this portion is key when converting to fractions because it represents the part of the whole that isn't complete.

Every digit in the fractional part has a specific place value that determines its fraction. For instance, each position after the decimal "." represents an increasing power of ten, commonly tenths, hundredths, thousandths, etc.

To convert a fractional decimal part into a fraction, identify its value by place. For 0.1, since the "1" is in the tenths place, it becomes \( \frac{1}{10} \). By understanding the place value system, any decimal's fractional part can be swiftly converted into its fraction equivalent, easing the transition from decimals to fractions.