Write each fraction as a decimal. For repeating decimals, write the answer by first using bar notation and then rounding to the nearest thousandth. 1/6

Verified step by step guidance

1. Identify the fraction to convert: \(\frac{1}{6}\).
2. Perform the division of the numerator by the denominator: divide 1 by 6 to find the decimal equivalent.
3. Recognize the repeating decimal pattern in the quotient. For \(\frac{1}{6}\), the decimal repeats a specific digit or group of digits.
4. Write the decimal using bar notation to indicate the repeating part. For example, if the digit 6 repeats, write it as \(0.1\overline{6}\).
5. Round the decimal to the nearest thousandth by looking at the fourth decimal place and adjusting the third decimal place 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 or a repeating decimal, depending on the denominator's factors.

Repeating Decimals and Bar Notation

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

Rounding Decimals to a Specific Place Value

Rounding decimals involves approximating a decimal number to a certain place value, such as the nearest thousandth. This means keeping three digits after the decimal point and adjusting the last digit based on the next digit's value.