Round each decimal to the nearest thousandth. (a) 0.8 (line above 8) (b) 0.4 (line above 4) (c) 0.9762 (d) 0.8645

Verified step by step guidance

1. Identify the decimal number that needs to be rounded.
2. Determine the place value to which you need to round the number. In this case, it's the thousandth place, which is the third digit to the right of the decimal point.
3. Look at the digit immediately to the right of the thousandth place to decide whether to round up or keep the digit the same. If this digit is 5 or greater, round up. If it's less than 5, keep the digit the same.
4. For repeating decimals, like 0.8 with a line above 8, recognize that the number is 0.888... and apply the same rounding rule.
5. Apply the rounding rule to each number: (a) 0.888..., (b) 0.444..., (c) 0.9762, and (d) 0.8645, and adjust the thousandth place accordingly.

Key Concepts

Rounding Decimals

Rounding decimals involves adjusting a number to a specified degree of precision, typically to make it simpler or easier to work with. When rounding to the nearest thousandth, you look at the digit in the fourth decimal place to determine whether to round up or down the third decimal place. If the fourth digit is 5 or greater, you increase the third digit by one; if it is less than 5, you leave the third digit unchanged.

Understanding Repeating Decimals

A repeating decimal is a decimal fraction that eventually repeats a digit or a group of digits indefinitely. In the context of rounding, it is important to recognize the repeating part, as it affects how you round the number. For example, 0.8 with a line above it (0.8̅) indicates that the 8 repeats indefinitely, which influences the rounding process.

Place Value

Place value refers to the value of a digit based on its position within a number. In decimals, the first digit to the right of the decimal point is the tenths place, the second is the hundredths place, and the third is the thousandths place. Understanding place value is crucial for accurately rounding numbers, as it helps identify which digit to round and how to adjust it based on the digits that follow.