Question

Evaluate each expression. $$ \begin{array}{l} \frac{5}{18} \\ \frac{11}{27} \end{array} $$

Short answer

0.278, 0.407

Step-by-step solution

- Convert \frac{5}{18} into a decimal

To convert \( \frac{5}{18} \) into a decimal, divide the numerator (5) by the denominator (18): \ 5 ÷ 18 = 0.2777... \ or approximately 0.278.

- Convert \frac{11}{27} into a decimal

To convert \( \frac{11}{27} \) into a decimal, divide the numerator (11) by the denominator (27): \ 11 ÷ 27 = 0.4074... \ or approximately 0.407.

Key concepts

Understanding the Numerator

The numerator is the top number in a fraction. It represents how many parts of the whole you have. For example, in the fraction \( \frac{5}{18} \), 5 is the numerator. It's like cutting a pizza into 18 slices and having 5 of those slices.
In long division, the numerator is what we are dividing. It goes inside the division bracket. Understanding the numerator helps us see what portion of the whole we are dealing with, which is essential in fraction to decimal conversions.

Defining the Denominator

The denominator is the bottom number in a fraction. It tells us into how many equal parts the whole is divided. In \( \frac{5}{18} \), 18 is the denominator. Think of it as the total number of pizza slices.
The denominator affects the size of the parts. A larger denominator means smaller parts. In division, the denominator goes outside the division bracket. Knowing the denominator is crucial for understanding how big each part is when converting a fraction to a decimal.

Explaining Long Division

Long division is a method used to divide two numbers, often used to convert fractions into decimals. For \( \frac{5}{18} \), we divide 5 by 18.
Here's how you can do it:

• Place 5 (the numerator) inside the division bracket.
• Place 18 (the denominator) outside the bracket.
• Perform the division step by step, bringing down zeros if needed.

This method helps you get a precise decimal value.

Understanding Approximation

Approximation is used when a division doesn't end neatly. Sometimes, the decimal goes on forever. For \( \frac{5}{18} \), the division gives us 0.2777...
To make it simpler, we round it to a certain number of decimal places. In this case, 0.278 is a rounded approximation. Approximation helps to represent the number in a more manageable form, while keeping it close to its real value.