Significant digits are the digits in a number that carry meaning contributing to its measurement resolution. For many applications, this is the final digit displayed in a result. When reporting results of a measurement, the number of significant digits is often taken to be the number of digits following the first non-zero digit in the original number. In scientific notation, all digits are significant since they contribute to the value of the exponent.
The term "significant digit" is also used in other contexts where it has a different definition. In statistics, for example, all digits are usually considered significant because they contribute to the precision of estimates.
In general, the significance of a digit decreases from left to right within a number. For example, in 123.45, the 1 is considered more significant than the 2, which is more significant than the 3, and so on. This is because each position within a number has a different weight or "place value".
The place value of a digit depends on its position within the number. In our example (123.45), the 1 is in the "ones" place, so its place value is 1; the 2 is in the "tens" place, so its place value is 10; and so on.
The significance of a digit also depends on its position within the number. In our example (123.45), all of the digits are significant because they're all in positions that contribute to the measurement's resolution (the ones place, tens place, etc.).
However, if we were to change our example to 1234.5, then only the first three digits would be considered significant because they're in positions that contribute to the measurement's resolution (the ones place, tens place, hundreds place). The 4 would not be considered significant because it's in a position that doesn't contribute to measurement resolution (the thousands place).
The same principles apply when Excel displays numbers with more than 15 digits.