Least significant digit
Sometimes abbreviated as LSD, the least significant digit of a number is the digit with the lowest exponent value, located in the rightmost position. For example, in the number 2516, the "6" is the least significant digit.
The "exponent value" refers to the power of the base number that is multiplied by each digit. For example, in base-10, "2516" represents (2 x 103) + (5 x 102) + (1 x 101) + (6 x 100), or 2000 + 500 + 10 + 6. Zero is the lowest exponent of 10 in this representation, therefore 6 is the least significant digit.
Denoting significance of trailing zeroes
If a number has trailing zeroes (such as "2600"), it may be necessary to indicate whether the zeroes are precise values ("significant"), or merely placeholders ("insignificant").
To represent unambiguously whether trailing zeroes are significant, the following notations can be used.
- Most commonly, the least significant precise digit may be overlined. For example, "2600" has three significant digits. The first three digits are reliable values. The least significant of these digits (the first zero) is overlined. The final zero is merely a placeholder to indicate the scale of the number.
- Less commonly, the least significant precise digit may be underlined. For example, "2600" has two significant digits, and the trailing zeroes are only placeholders. The least significant digit (6) is underlined.
- To indicate unambiguously that all trailing zeroes are significant, the number can be terminated with a decimal point (period). For example, if "2600." were used in an equation, it would indicate "precisely twenty-six hundred."
The number 2600 could be described as "precise to the nearest ten." Similarly, the number 2600 could be described as "precise to the nearest hundred."