Why isn't the zero after the decimal in $0.01$ significant?

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Why isn't the zero after the decimal in $0.01$ significant? Although it is pretty obvious that the zero before the decimal is insignificant, I don't understand why the zero after the decimal is not significant.

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1 Answer

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Significant figures are used to denote the precision of a measurement. The leading zeros are not significant because they don't give us information about the precision of the measurement.

Let's say you measure something with a meter stick that only has centimeter markings (no millimeters). You get that the object is $8.5 cm$ long, but you want to use your measurement a formula that expects units of meters. When you convert from $8.5 cm$ to $0.085 m$, you haven't improved the precision of the measurement, but you gain the leading zeros.

For more information:

• This significant figures overview talks about how significant figures are tied to the precision of measurements, with an introduction that covers the meaning of precision (and how it's not the same as accuracy).
• See this helpful video from KhanAcademy

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