Question

Find a decimal equivalent for each fraction or mixed number. \(\frac{16}{5}\)

Short answer

3.2

Step-by-step solution

Understand the problem

We need to convert the fraction \(\frac{16}{5}\) into a decimal number.

Set up the division

To convert a fraction to a decimal, divide the numerator by the denominator. In this case, divide 16 by 5.

Perform the division

Divide 16 by 5. \(\frac{16}{5} = 3.2\).

Verify the result

Multiply the decimal result by the denominator to check if it equals the numerator: \(3.2 \times 5 = 16\). The calculation is correct.

Key concepts

decimal representation

When we talk about a decimal representation, we're referring to expressing a number in its decimal form. This can be done by converting fractions, such as \(\frac{16}{5}\), into a decimal. Decimals are another way to show parts of a whole number. This is important in real-life applications, such as measuring quantities, money, and calculations. By converting the fraction \(\frac{16}{5}\) into a decimal, we get 3.2. This means that \(\frac{16}{5}\) is equal to 3.2 when expressed as a decimal.

division

To convert a fraction to a decimal, we need to understand the process of division. Dividing the numerator (top number) by the denominator (bottom number) will give us the decimal result. Let's break it down with our example, \(\frac{16}{5}\):

• Firstly, identify the numerator (16) and the denominator (5).
• Next, set up the division: 16 divided by 5.
• Perform the division. When you divide 16 by 5, you get 3.2.

This method can be employed for any fraction. It's essential to note that division might sometimes result in a repeating or a terminating decimal, such as 3.2.

numerator and denominator

Understanding the terms numerator and denominator is crucial in the fraction to decimal conversion process. The numerator is the top number of the fraction, representing how many parts we have. The denominator is the bottom number and shows into how many parts the whole is divided. For \(\frac{16}{5}\):

• The numerator is 16. It shows that we have 16 parts.
• The denominator is 5. It signifies that each unit is divided into 5 equal parts.

When we divide 16 by 5, we equally distribute 16 parts into 5 groups, giving us a decimal result of 3.2. Always ensure that you clearly identify the numerator and denominator to perform correct calculations.