Significant Figures and Decimal Places

The number of digits after the decimal point is determined simply by counting them. For example, the number 478.32 is given to two decimal places. 

The number of significant figures is a harder quantity to determine, but we can start by applying some simple rules. 

Leading zeros are never significant. For example, the number 0.005 32 contains three significant digits. 

More problematic is the case of trailing zeros. For example, we may not know whether the number 500 represents 500 exactly, or is 502 rounded to the nearest 10, or 521 rounded to the nearest hundred. We have to consider each case individually, depending on what other information is available and using our discretion. If, however, the trailing zeros appear after a decimal point they are significant - because omitting them only changes the precision with which the number is quoted. 

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