math

Round to the Nearest Thousandth Calculator

Q: What is the difference between rounding to the nearest hundredth and nearest thousandth?

Rounding to the nearest hundredth keeps two decimal places, while rounding to the nearest thousandth keeps three. The hundredth place is the second position after the decimal; the thousandth is the third. For 5.6789, rounding to the nearest hundredth gives 5.68, whereas rounding to the nearest thousandth gives 5.679. Use hundredths for money or simpler measurements; use thousandths when greater precision is required, such as in chemistry or precision engineering.

Q: How do I round 38.7165 to the nearest thousandth?

Identify the thousandth position (the third decimal): 6. Then identify the digit to its right (the fourth decimal): 5. Since 5 is the threshold, round half up means you increase the thousandth digit by 1. The result is 38.717. This same principle applies regardless of the value's magnitude or whether it's positive or negative.

Q: Why would I use banker's rounding instead of round half up?

Banker's rounding (round half to even) is preferred in statistical and financial work because over many rounding operations, it introduces less systematic bias. When you always round 0.5 up, you gradually inflate aggregate values. Banker's rounding alternates the direction, keeping long-term averages more accurate. It's less common in everyday use but valuable in data science and accounting.

Q: Can I round a number that already has fewer than three decimal places?

Yes. If you round 5.25 to the nearest thousandth, the answer is 5.250. Rounding to the nearest thousandth means expressing the number with exactly three decimal places (or fewer if trailing zeros are dropped by convention). No information is lost; you're simply expressing the same value at that precision level.

Q: What happens when rounding introduces a carry to the whole number?

If the thousandth digit is 9 and the fourth decimal is 5 or higher, rounding up changes that 9 to 10, which carries over to the hundredths place. This cascade can eventually reach the whole number. For example, 4.9995 rounded to the nearest thousandth becomes 5.000, as the carry propagates leftward through each decimal position.

Q: How does truncation differ from rounding?

Truncation simply removes all digits beyond the desired precision without checking the next digit. It never rounds up. For instance, truncating 5.6789 to three decimals gives 5.678, whereas rounding would give 5.679. Truncation is useful when you want a conservative estimate or must guarantee a value doesn't exceed a threshold, but it discards information and is rarely used in standard mathematics.

Rounding to the nearest thousandth means keeping exactly three digits after the decimal point. This is essential in scientific contexts, financial calculations, and engineering where precision matters but excessive decimal places clutter results. Enter your number and select your preferred rounding method—the calculator handles the work and displays the outcome immediately.

Last updated: May 9, 2026

Creators Anna Szczepanek, PhD Mathematics

Reviewers Mateusz Mucha and Jasmine J. Mah

2,045 people find this calculator helpful

Understanding Thousandth-Place Rounding

The thousandth position is always the third digit to the right of the decimal point. When rounding to this precision level, you examine the fourth decimal place to decide whether to round up or down.

Locate the thousandth digit: Count three places after the decimal.
Check the digit to its right: This fourth decimal place determines your action.
Apply standard rounding rules: If that digit is 4 or lower, leave the thousandth digit unchanged. If it's 5 or higher, increase the thousandth digit by one.

For example, 0.4286 becomes 0.429 because the fourth decimal (6) exceeds 4. Similarly, 7.1234 rounds down to 7.123 since the fourth decimal (4) is below 5.

Rounding to the Nearest Thousandth Formula

The rounding process depends on identifying the digit in the thousandth position and the digit immediately to its right. The core logic applies across all rounding methods.

If (fourth decimal digit) < 5: keep the thousandth digit as is

If (fourth decimal digit) ≥ 5: add 1 to the thousandth digit

Thousandth digit — The third position after the decimal point
Fourth decimal digit — The digit immediately following the thousandth position; determines rounding direction

Common Rounding Methods

Different disciplines and contexts use varied approaches to rounding, especially when the fourth decimal is exactly 5.

Round half up: The most common method taught in schools. When the digit is 5 or higher, round up; otherwise, round down.
Round half down: The reverse of above. Use this when you want to avoid inflating values unnecessarily.
Round half to even (banker's rounding): If the digit is 5, round to the nearest even thousandth digit. This minimises bias over large datasets.
Truncation: Simply cut off everything beyond three decimals without rounding. Use this for conservative estimates.

Choose the method that suits your application. Scientific work often prefers banker's rounding, while casual calculations typically use round half up.

Practical Examples

Let's walk through several scenarios to cement the process:

38.7165: The thousandth digit is 6; the fourth decimal is 5. Rounding half up gives 38.717.
12.3334: The thousandth digit is 3; the fourth decimal is 4. Since 4 < 5, the result is 12.333.
0.9996: The thousandth digit is 9; the fourth decimal is 6. Since 6 ≥ 5, you round up: 1.000.
−5.4445: Negative numbers follow the same rules. The fourth decimal is 5, so rounding half up changes the thousandth digit from 4 to 5, yielding −5.445.

Key Rounding Pitfalls to Avoid

Precision errors and misunderstandings often arise when rounding. Watch out for these common mistakes.

Forgetting the fourth decimal exists — The rounding decision hinges entirely on the digit in the fourth position. Many people focus only on the thousandth place and forget to check what comes next. Always pause and identify that fourth digit before applying your rounding rule.
Confusing thousandths with tenths or hundredths — Tenths are one place after the decimal; hundredths are two places. Thousandths are three. Misidentifying which position you're rounding to will produce an entirely wrong result. Count carefully.
Rounding multiple times in succession — If you must round an intermediate result and then round again, errors compound. Whenever possible, keep full precision during calculations and round only the final answer to avoid cumulative drift.
Assuming all methods produce the same result — When the fourth decimal is exactly 5, different rounding methods disagree. Know which method your field standard requires—truncation, round half up, and banker's rounding can yield different thousandth values.

Frequently Asked Questions

What is the difference between rounding to the nearest hundredth and nearest thousandth?

Rounding to the nearest hundredth keeps two decimal places, while rounding to the nearest thousandth keeps three. The hundredth place is the second position after the decimal; the thousandth is the third. For 5.6789, rounding to the nearest hundredth gives 5.68, whereas rounding to the nearest thousandth gives 5.679. Use hundredths for money or simpler measurements; use thousandths when greater precision is required, such as in chemistry or precision engineering.

How do I round 38.7165 to the nearest thousandth?

Identify the thousandth position (the third decimal): 6. Then identify the digit to its right (the fourth decimal): 5. Since 5 is the threshold, round half up means you increase the thousandth digit by 1. The result is 38.717. This same principle applies regardless of the value's magnitude or whether it's positive or negative.

Why would I use banker's rounding instead of round half up?

Banker's rounding (round half to even) is preferred in statistical and financial work because over many rounding operations, it introduces less systematic bias. When you always round 0.5 up, you gradually inflate aggregate values. Banker's rounding alternates the direction, keeping long-term averages more accurate. It's less common in everyday use but valuable in data science and accounting.

Can I round a number that already has fewer than three decimal places?

Yes. If you round 5.25 to the nearest thousandth, the answer is 5.250. Rounding to the nearest thousandth means expressing the number with exactly three decimal places (or fewer if trailing zeros are dropped by convention). No information is lost; you're simply expressing the same value at that precision level.

What happens when rounding introduces a carry to the whole number?

If the thousandth digit is 9 and the fourth decimal is 5 or higher, rounding up changes that 9 to 10, which carries over to the hundredths place. This cascade can eventually reach the whole number. For example, 4.9995 rounded to the nearest thousandth becomes 5.000, as the carry propagates leftward through each decimal position.

How does truncation differ from rounding?