Problem 96 - Prealgebra

Question

Write as a decimal. $$\frac{3}{16}$$

Step-by-Step Solution

Answer

The decimal equivalent of \( \frac{3}{16} \) is 0.1875.

Step 1: Understanding the Fraction

The given fraction is \( \frac{3}{16} \). Our job is to solve this to find its decimal equivalent.

Step 2: Perform Division

Divide the numerator, 3, by the denominator, 16. This division can be worked out manually or using a calculator. Performing this division gives us a decimal value as follows: When 3 is divided by 16, it is approximately equal to 0.1875.

Step 3: Verify the Decimal

To ensure the conversion to a decimal is correct, multiply 0.1875 by 16 to check if the result gives approximately 3. \( 0.1875 \times 16 = 3 \). This confirms the decimal is correct.

Key Concepts

Decimal Representation

Decimal representation is a way of expressing fractions in terms of a decimal point, making them easier to read and compare. While fractions are represented as two numbers divided (the numerator over the denominator), converting them to decimals involves identifying what part of a whole these fractions represent in base 10. In the case of the fraction \( \frac{3}{16} \), its decimal representation is 0.1875. To understand it simply:

• Decimals break down these fractions into parts of ten, hundred, thousand, and so on.
• This makes doing math operations like addition and comparison far more straightforward, since decimals have a uniform base of ten.

Thus, one reason we convert fractions to decimals is to make calculations easier and more intuitive, especially when dealing with various fractions.

Long Division

Long division is a manual method for dividing one number by another. It's particularly useful for finding the decimal representation of fractions without relying on a calculator. Understanding long division is crucial when you do not have a calculator on hand, or when you are striving for a better grasp of the arithmetic involved. To find the decimal representation of \( \frac{3}{16} \) through long division, follow these steps:

• 3, which is the numerator, is divided into the denominator, 16.
• Since 3 is less than 16, you need to find how many 16s fit into 30, 300, and so forth.
• This division results each time will give you a digit of the decimal.

Performing these steps, you'll discover each subsequent digit contributes to the building of the decimal portion. It requires a bit of practice, but once mastered, it's a very reliable tool for number conversion.

Numerator and Denominator

Understanding the terms numerator and denominator is essential in comprehending how fractions function and how to convert them into decimals. The numerator and denominator are the two parts of a fraction:

• The numerator is the top number and signifies the number of parts considered.
• The denominator is the bottom number and tells you into how many parts the whole is divided.

For \( \frac{3}{16} \):

• The numerator, 3, indicates that we have 3 parts of the whole.
• The denominator, 16, tells us that there are 16 equal parts in that whole.

By dividing the numerator by the denominator, we transition from a fraction, which is a part-over-part representation, to a decimal form, which is a base-10 representation. This shift helps us visualize fractions better, especially when comparing or calculating them, thus making operations more accessible. The understanding of how a fraction's top and bottom numbers interact is key to mastering fraction-to-decimal conversions.