Rounding is the process of reducing the number of significant digits in a number while keeping its value close to the original. We round numbers to make them simpler and easier to work with, especially when exact precision isn't necessary or when we want to avoid suggesting false precision in measurements. Rounding is used everywhere: estimating costs, reporting statistics, expressing measurements, and simplifying calculations.

The Basic Rounding Rule

To round a number, identify the place value you're rounding to, then look at the digit immediately to the right (the "deciding digit"):

• If the deciding digit is 5 or greater (5, 6, 7, 8, 9): Round UP - increase the rounding digit by 1
• If the deciding digit is less than 5 (0, 1, 2, 3, 4): Round DOWN - keep the rounding digit the same
• All digits to the right of the rounding position become zero (or are dropped if after a decimal point)

Example: Round 347 to the nearest ten
• Rounding digit: 4 (in the tens place)
• Deciding digit: 7 (in the ones place)
• Since 7 ≥ 5, round UP: 347 rounds to 350

Common Rounding Positions

• Nearest whole number: Look at the tenths place (first digit after decimal)
• Nearest ten: Look at the ones place
• Nearest hundred: Look at the tens place
• Nearest tenth: Look at the hundredths place (second decimal digit)
• Nearest hundredth: Look at the thousandths place (third decimal digit)

The Special Case of 5

When the deciding digit is exactly 5 (with no digits or only zeros after it), there are different conventions:

• Standard rule: Always round up (most common in everyday use)
• Banker's rounding: Round to the nearest even number (reduces bias in statistical calculations)
• Example with standard rule: 2.5 → 3, and 3.5 → 4
• Example with banker's rounding: 2.5 → 2 (nearest even), and 3.5 → 4 (nearest even)

Significant Figures

Rounding to a specific number of significant figures means keeping that many meaningful digits, counting from the first non-zero digit. This is important in science and engineering to indicate measurement precision. For example, 0.004567 rounded to 3 significant figures is 0.00457.