# Rounding and Significant Digits

### In both descriptive and inferential statistics, statisticians report numbers, both in tables and in prose. Typically, when we report measurements or calculations we must round our numbers. In rounding, we are often guided by the concept of significant digits: the number of digits starting at the first non-zero digit and counting to the right. For example, the number 456 has three significant digits, while 456.00 has five. The waters become a bit muddy when we are dealing with large whole numbers such as 13,000. 13,000 may have two significant digits or it may have five. 13,000.0 suggests six significant digits. To clarify, scientific notation is often used: 13,000 may be represented by 1.3 E4 or 1.3*10^{4}.

### How we round often depends on the precision of the data we collect. For example, if we measure the width of a blue crab, we could measure her 10 cm, 10.1 cm, 10.12 cm, etc. Let’s say that our caliper only allows us to measure to the 1/10th of a centimeter and we need to calculate a mean width of ten blue crabs. Would it be appropriate to the report the mean as 10.3748 cm? No, as this would be reporting a mean that is falsely precise. One frequently used rule of thumb is to round a mean (or a standard deviation) to one additional decimal than the data. So in our case, we would report the mean width of the ten crabs to be 10.37cm.

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