Thousandths
Thousandths is the third decimal place value, representing one part out of one thousand equal parts.
Formula
1 \text{ thousandth} = \frac{1}{1000} = 0.001
Definition
Thousandths is the third place after the decimal point: one thousandth ($0.001$) is one piece when you split $1$ into $1{,}000$ equal parts, a very small amount. Formally, the thousandths place has place value $10^{-3} = 0.001$, and metric prefixes map directly to decimal places (milli- means thousandths, so $0.001$ meter is $1$ millimeter); rounding to the nearest thousandth is common in scientific measurement. The thousandths digit is $\lfloor 1000x \rfloor \bmod 10$, and in numerical analysis the number of decimal places carrying meaningful information relates to significant figures and machine epsilon, the minimum representable difference from $1.0$ in a given floating-point precision.
Example
$0.375$ has a $5$ in the thousandths place ($3$ tenths, $7$ hundredths, $5$ thousandths), and the fraction $3/8 = 0.375$ exactly. Rounding $0.1379$ to the nearest thousandth: look at the ten-thousandths digit ($9 \ge 5$) and round up to $0.138$, the same precision chemists use when reporting molar masses. IEEE 754 single precision carries about $7$ significant decimal digits and double precision about $15$-$17$, so thousandths precision is well within both, though differences near $10^{-15}$ sit at the very limit of double precision.
Key Insight
Thousandths appear throughout science and medicine, a millimeter is a thousandth of a meter, and understanding them helps with precision in real-world measurements. All fractions $a/b$ where $b$ divides $1000$ terminate at or before the thousandths place, bridging fraction arithmetic and decimal place value. The interplay between decimal place values and floating-point precision determines the accuracy of numerical algorithms; error analysis in scientific computing tracks how errors at the thousandths place (or deeper) propagate through computation, a field called numerical stability.