Write each fraction as a decimal. For repeating decimals, write the answer by first using bar notation and then rounding to the nearest thousandth. 3/8

Verified step by step guidance

1. Identify the fraction given: \( \frac{3}{8} \). Our goal is to convert this fraction into a decimal form.
2. Perform the division of the numerator by the denominator: divide 3 by 8. This can be done using long division or a calculator.
3. Check if the decimal terminates or repeats. Since 8 is a power of 2 (\( 2^3 \)), the decimal will terminate.
4. Write the decimal result from the division. Since it terminates, there is no repeating part, so bar notation is not needed.
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 either a terminating decimal, which ends after a finite number of digits, or a repeating decimal, where one or more digits repeat indefinitely.

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, making it easier to represent and understand the decimal's pattern.

Rounding Decimals to a Specific Place Value

Rounding decimals involves approximating a decimal number to a specified place value, such as the nearest thousandth. This is done by looking at the digit immediately after the target place and adjusting the last retained digit accordingly to simplify the number.