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1Repair Windows errors before they cause bigger problems2Scan for outdated or missing drivers - takes under a minute3Clear out junk files and repair common Windows errorsThe least significant digit (LSD) is the digit in a positional number with the lowest place value. In an ordinary whole number, it is the rightmost digit: in 6,703, the LSD is 3, the units digit. “Least significant” refers to place value, not to which digit looks smallest.
How to identify the least significant digit
Read a positional number from left to right: each place has a weight determined by the number system’s base. The digit occupying the place with the lowest weight is the LSD. For a conventional base-10 integer, that place is the units place at the far right.
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For example, in 6,703, 6 represents thousands, 7 hundreds, 0 tens, and 3 units. The LSD is 3. It would still be the rightmost digit if the number ended in zero: in 6,700, the place-value LSD is 0.
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How the term relates to binary
The same idea applies in other positional systems. In a binary number, the rightmost digit has the lowest place value and is commonly called the least significant bit (LSB). “Bit” is the usual name for a binary digit.
Why measurement notation can make “significant digit” confusing
In measurement and significant-figure discussions, “least significant digit” may refer to the final digit treated as meaningful in the stated precision. That is related to, but not identical with, the place-value definition for an integer.
The U.S. Department of Energy’s Fundamentals Handbook, Mathematics, Volume 1 gives a convention in which the rightmost nonzero digit is the last significant digit when a number has no decimal point; when a decimal point is present, the rightmost digit counts, even if it is zero. Under that convention, 7 is the last significant digit in 3270, while 0 is the last significant digit in 27.620.
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Outbyte PC Repair FREERepair Windows errors before they cause bigger problemsFix Now →Outbyte Driver Updater FREEScan for outdated or missing drivers - takes under a minuteDriver Scan →These statements answer different questions. The place-value LSD of the integer 3270 is its final written digit, 0. The handbook’s measurement convention identifies 7 as the last significant digit in the notation 3270. A trailing zero in a whole-number measurement can leave precision unclear unless the notation makes the intended precision explicit.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.How least-significant-digit rules affect rounding measurements
Rules for reporting measured calculations depend on the operation; they do not change the definition of an LSD in positional notation.
- Addition and subtraction: Round the result to the place value of the least precise measurement.
- Multiplication and division: Report no more significant figures than are present in the least precise factor.
For a measured value, the size of its least significant place also helps indicate the scale of the measurement’s absolute error, as discussed by Cornell’s Virtual Lab. Follow the precision conventions required by the context when reporting a result.
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