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 increase the third decimal place by one; if it is less than 5, you leave the third decimal place unchanged.

Place Value

Place value refers to the value of a digit based on its position within a number. In decimal numbers, each position to the right of the decimal point represents a fractional value, with the first position being tenths, the second hundredths, and the third thousandths. Understanding place value is crucial for accurately rounding numbers, as it helps identify which digit to adjust based on the rounding rules.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. When rounding, it is important to consider significant figures to maintain the integrity of the number's precision, especially in scientific and mathematical contexts where accuracy is critical.