Significant Numbers in Experiments

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I don't understand why data has to be in a specific significant numbers? Why significant numbers? Can't it be decimal places with the appropriate unit? What if you multiply two values with different sig figs? Why the answer should follow the least sig fig value? Why not decimal places?
 

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The most important thing in scientific data is error bars; nothing is more useless than an experimental result for which you do not know how accurate or imprecise the measurement was, and such cannot identify an incorrect theory.

But in school people aren't so picky about errors, so instead of writing 129.4+/-9.2 (or, more loosely, 1.3+/-0.1 x 10^2), they might just write 1.3x10^2 (2. sig. fig's). Obviously you can't just write 130 (or worse, 130.000) because that could be mistakenly interpretated as "129.5 to 130.5". Decimal places aren't a sure indicator of anything, and what matters is that you learn the habit of considering uncertainty.

When you multiply an exactly known number by an imprecise one, the answer is obviously not exactly known. There are a few different ways to correctly calculate the uncertainty in the product of two measurements, but the absolute simplest rule of thumb is just to maintain the least number of significant figures.
 
Chronos
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The sum of the squares method is effective for most direct measurements. Square the individual errors, add them up and take the square root. This can, however, lead to deceptive results. It assumes all error sources are independent [i.e., tend to cancel one another out]. This is not necessarily true - e.g., feedback in an amplifier circuit.
 

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