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The least significant digit (LSD) is the digit in a positional number that has the lowest place value. In an ordinary whole number, it is the rightmost digit: in 6703, the LSD is 3, the units digit.
How to find the least significant digit
Read the number’s place values from left to right. The digit with the smallest positional weight is the LSD. In base 10, the rightmost place in a whole number is the units place, so its digit is the LSD. Cambridge University Press describes the rightmost digit as having the lowest weight in positional notation (Cambridge University Press).
For example, in 6703, 6 represents thousands, 7 hundreds, 0 tens, and 3 units. The LSD is 3. It is not necessarily the smallest digit by numerical value: the 0 in the tens place is smaller as a symbol, but that position has a greater place value than the units position.
Least significant digit in decimal and binary
The idea applies to positional systems in any base. In a base-10 integer, the units digit is the LSD. In a binary number, the rightmost position has the lowest place value and is commonly called the least significant bit (LSB). The digit in that position is the binary number’s LSD.
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Why significant figures use the term differently
In measurement, “least significant digit” can refer to the last digit that communicates the precision of a written quantity. That convention is about significant figures, not simply the lowest place-value position in an integer. A U.S. Department of Energy mathematics handbook treats the rightmost nonzero digit as the last significant digit when a number has no decimal point, but treats the rightmost digit as significant when a decimal point is present, even if it is zero (DOE Fundamentals Handbook, Mathematics, Volume 1).
This distinction matters for trailing zeros. In the written integer 3270, the place-value LSD is 0, while the handbook’s significant-figure convention identifies 7 as the last significant digit. In 27.620, the final 0 is significant under that convention. North Carolina environmental guidance gives a similar example: it identifies 8 as the last significant figure in 5800 and 0 in 43.120 (North Carolina environmental guidance).
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If a measurement’s precision matters, use notation that states it clearly, such as scientific notation or a decimal point where appropriate. That avoids treating an ambiguous trailing zero as though it communicates a precision that was never specified.
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How the LSD relates to rounding measurements
The positional definition does not change the rules for reporting measured calculations. For sums and differences, Texas Gateway advises rounding to the place value of the least accurate measurement. For products and quotients, the result should have no more significant figures than the least precise factor (Texas Gateway: Significant Figures).
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In measurement work, the unit size represented by the least significant digit can also help describe the reading’s resolution and associated absolute error; Cornell’s Virtual Lab discusses this relationship in its measurement material (Cornell Virtual Lab).
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