Thousandth Rounding Tool

Enter Number

Common Examples: Rounding to Nearest Thousandth

Original Number	Rounded to Thousandth	Explanation
3.14159265	3.142	Fourth decimal (5) rounds up
0.123456	0.123	Fourth decimal (4) < 5, rounds down
2.7182818	2.718	Fourth decimal (2) < 5, rounds down
0.9999	1.000	Rounds up to 1
5.6789	5.679	Fourth decimal (9) ≥ 5, rounds up
0.0005	0.001	Fourth decimal (5) rounds up

How to Round to the Nearest Thousandth

Rounding to the nearest thousandth means keeping exactly three digits after the decimal point. This precision level is essential in scientific calculations, engineering work, precise measurements, and advanced mathematics.

Why Round to the Nearest Thousandth?

Scientific Precision: Standard precision for many scientific calculations
Engineering: CAD drawings and specifications often use 3 decimals
Chemistry: Molarity and concentration calculations
Physics: Precise measurements and constants (e.g., π = 3.142)
Statistics: Higher precision for correlation coefficients and p-values

Step-by-Step Rounding Process

Step 1: Identify the Third Decimal Place

In the number 3.14159, the third decimal place is "1" (the thousandths position).

Step 2: Look at the Fourth Decimal

The fourth decimal digit determines rounding direction. In 3.14159, the fourth decimal is "5".

Step 3: Apply the Rounding Rule

If the fourth decimal is 5 or greater, round UP. If less than 5, round DOWN. Since 5 rounds up, result is 3.142.

Step 4: Keep Exactly Three Decimals

Drop all digits after the third decimal place. Final result: 3.142

Common Use Cases

Pi (π): 3.14159265... rounds to 3.142 (nearest thousandth)

Euler's Number (e): 2.71828182... rounds to 2.718

Molarity: 0.123456 M solution rounds to 0.123 M

Measurements: 15.6789 cm rounds to 15.679 cm

Exchange Rates: 1.23456 USD/EUR rounds to 1.235 for precision trading

Understanding Thousandths

Place value: The thousandths place represents 1/1000 or 0.001

Decimal positions: First = tenths (0.1), Second = hundredths (0.01), Third = thousandths (0.001)

Precision level: Thousandths are 10× more precise than hundredths

Academic Applications

Calculus: Limits and derivatives often expressed to 3 decimals

Probability: P-values in statistics (e.g., p = 0.042)

Chemistry Labs: pH values, concentrations, and yields

Quick Reference

What is a thousandth? One thousandth = 1/1000 = 0.001 = three decimal places

Key digit: Look at the fourth decimal place (ten-thousandths)

Standard use: Science, engineering, advanced math, and precision measurements