Write each fraction as a decimal. For repeating decimals, write the answer by first using bar notation and then rounding to the nearest thousandth. 5/9

Verified step by step guidance

1. Step 1: Understand that to convert a fraction to a decimal, you need to perform division. Here, divide 5 by 9.
2. Step 2: Set up the division of 5 by 9. Since 5 is less than 9, you will need to add a decimal point and zeros to 5 to perform the division.
3. Step 3: Perform the long division. Notice that after a few steps, the remainder starts repeating, indicating a repeating decimal.
4. Step 4: Identify the repeating part of the decimal. Use bar notation to represent the repeating sequence.
5. Step 5: Round the repeating decimal to the nearest thousandth by considering the digits up to the fourth decimal place.

Key Concepts

Fractions and Decimals

Fractions represent a part of a whole and can be converted into decimals. The numerator indicates how many parts are taken, while the denominator shows the total number of equal parts. Understanding this relationship is crucial for converting fractions like 5/9 into their decimal form.

Repeating Decimals

Repeating decimals occur when a decimal representation of a fraction has one or more digits that repeat indefinitely. For example, 5/9 converts to 0.555..., where '5' repeats. Bar notation is used to denote this repetition, such as 0.5̅, indicating that the '5' continues infinitely.

Rounding Decimals

Rounding decimals involves adjusting the decimal to a specified number of places, which simplifies the number while maintaining its value. When rounding to the nearest thousandth, you look at the digit in the fourth decimal place to determine whether to round up or down. This is essential for providing a concise answer when dealing with repeating decimals.