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. Start by understanding that to convert a fraction to a decimal, you divide the numerator by the denominator. Here, divide 5 by 9.
2. Perform the division 5 \(\div\) 9. Since 5 is less than 9, the decimal will be less than 1, so add a decimal point and zeros to continue the division.
3. Recognize that the decimal expansion of 5/9 will be a repeating decimal because 9 is a factor that produces repeating decimals when dividing numbers not multiples of 9.
4. Identify the repeating digit(s) in the decimal expansion and write the decimal using bar notation to indicate the repeating part. For example, if the decimal repeats '5', write it as 0.\(\overline{5}\).
5. Finally, round the decimal to the nearest thousandth (three decimal places) by looking at the fourth decimal place and adjusting accordingly.

Key Concepts

Converting Fractions to Decimals

Converting a fraction to a decimal involves dividing the numerator by the denominator. This process can result in a terminating decimal, which ends, or a repeating decimal, where one or more digits repeat indefinitely.

Repeating Decimals and Bar Notation

A repeating decimal has digits that repeat in a pattern infinitely. Bar notation is used to indicate the repeating part by placing a horizontal bar over the repeating digits, clearly showing which digits repeat.

Rounding Decimals to a Specific Place Value

Rounding decimals involves approximating a decimal number to a certain place value, such as the nearest thousandth (three decimal places). This is done by looking at the digit immediately after the desired place and adjusting accordingly.