91Ó°ÊÓ

Converting fractions to decimals is a crucial skill in math. To convert a fraction like \(\frac{2}{3}\), you perform division. This means you divide the numerator (2) by the denominator (3). In this case, \(2 ÷ 3 = 0.666\), which is a repeating decimal. To represent a repeating decimal, a bar is placed over the repeating digits, making it \(0.666\text{ (repeating)}\). Understanding how to perform this conversion helps in comparing numbers more easily. For example, if the exercise gives you a fraction, converting it to a decimal makes it simpler to determine if one number is greater or less than another.

Comparing decimals involves looking at the value of each digit. Start from the leftmost digit and move to the right. When comparing \(0.66\) and \(0.666\text{ (repeating)}\), first look at the tenths place. Both numbers have a 6 in the tenths place. Next, compare the hundredths place. Both numbers also have a 6 there.
However, \(0.666\text{ (repeating)}\) has an additional 6 in the thousandths place that goes on infinitely. Because \(0.666\text{ (repeating)}\) extends beyond two decimal places, it is slightly larger than \(0.66\). Therefore, the correct comparison in this scenario is \(0.66 < 0.666\text{ (repeating)}\). When comparing decimals, always look at each place value step by step.

Inequality symbols help express the relative size of two values. There are several key symbols to understand:

• \(<\) which means 'less than'
• \(>\) which means 'greater than'
• \(=\) which means 'equal to'

In this exercise, since \(0.66\) is less than \(\frac{2}{3}\), we use the \( < \) symbol. Therefore, the correct inequality is \( 0.66 < \ \frac{2}{3}\). Recognizing and using the correct inequality symbol is essential for accurately conveying the relationship between numbers. These symbols are fundamental in many areas of mathematics and everyday problem-solving scenarios.