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

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.