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 accuracy, typically to the nearest whole number, tenth, hundredth, or thousandth. When rounding to the nearest thousandth, you look at the digit in the fourth decimal place to determine whether to round up or down. If this digit is 5 or greater, you round up; if it is less than 5, you round down.

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 can affect the rounding process. For example, 0.8 with a line above it indicates that the 8 repeats, which influences how you round it to the nearest thousandth.

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 consider when rounding.