Problem 76 - Prealgebra

Question

Write each fraction or mixed number as a decimal. \(1 \frac{1}{16}\)

Step-by-Step Solution

Answer

The decimal is 1.0625.

Step 1: Identify the Mixed Number

We have the mixed number \(1 \frac{1}{16}\), which consists of a whole number (1) and a fraction (\(\frac{1}{16}\)).

Step 2: Convert the Fraction to Decimal

To convert the fraction \(\frac{1}{16}\) to a decimal, divide the numerator (1) by the denominator (16): \[\frac{1}{16} = 0.0625\]

Step 3: Add the Whole Number and Decimal

Add the decimal obtained from the fraction to the whole number from the mixed number:\[1 + 0.0625 = 1.0625\]

Step 4: Conclusion: Final Decimal

Thus, the mixed number \(1 \frac{1}{16}\) as a decimal is \(1.0625\).

Key Concepts

Mixed Numbers

A mixed number is a combination of a whole number and a fraction. It's a way to represent values that fall between whole numbers. For instance, the mixed number \(1 \frac{1}{16}\) consists of the whole number 1 and the fraction \(\frac{1}{16}\). Mixed numbers can also be thought of as sums, where we simply add the whole number to the fraction's value.

• The whole number part provides a base value or whole units of measurement.
• The fraction part adds an extra amount that is less than one.

Understanding mixed numbers is essential when transitioning between fractions and decimals, especially because their conversion steps form the basis of many mathematical concepts.

Decimal Conversion

Decimal conversion is the process of changing fractions or mixed numbers into decimals. This conversion involves basic division, where you divide the numerator (the top number) by the denominator (the bottom number).
For example, with the fraction \(\frac{1}{16}\), we divide 1 by 16 to get 0.0625. This value represents the fractional part of the mixed number when expressed as a decimal.

• Decimals are easier to use for calculations compared to fractions.
• They also provide a universal approach to representing values, as most calculators and computer systems use decimals.

Converting mixed numbers involves converting the fractional part first, then adding this decimal to the whole number portion.

Fractions

Fractions are mathematical expressions that describe parts of a whole. They consist of two parts: a numerator and a denominator. The numerator represents the number of equal parts we have, and the denominator indicates the total number of those parts in a whole.
When dealing with fractions like \(\frac{1}{16}\), we often convert them to decimals for easier handling in mathematical operations.

• Fractions provide a clear picture of division and proportion.
• They are crucial in various real-life situations, such as measuring ingredients in cooking or determining probabilities in statistics.

Understanding how to manipulate fractions and convert them to other forms like decimals is an essential skill in mathematics.