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. 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.
4. If the digit to the right is 5 or greater, increase the thousandth place digit by 1. If it's less than 5, keep the thousandth place digit the same.
5. Apply this rounding rule to each of the given numbers: (a) 0.888..., (b) 0.444..., (c) 0.9762, and (d) 0.8645.

Key Concepts

Rounding Rules

Rounding is the process of adjusting the digits of a number to make it simpler while keeping its value close to the original. The basic rule is to look at the digit immediately to the right of the place value you are rounding to. If this digit is 5 or greater, you round up; if it is less than 5, you round down.

Decimal Places

Decimal places refer to the number of digits to the right of the decimal point. In this question, rounding to the nearest thousandth means you focus on the third digit after the decimal. Understanding how to identify and manipulate decimal places is crucial for accurate rounding.

Repeating Decimals

A repeating decimal is a decimal fraction that eventually repeats a digit or a group of digits indefinitely. In the context of this question, the notation with a line above a digit indicates that the digit repeats. Recognizing and handling repeating decimals is important for accurate rounding and representation.