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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.

Shaurya Gupta
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    A very informal answer: $1$ cm has one significant digit. If we measure in metres, we get $0.01$. No added accuracy! – André Nicolas Apr 14 '14 at 05:14
  • @AndréNicolas That'll help...Thanks. – Shaurya Gupta Apr 14 '14 at 05:16
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    But if you measure the same one-centimeter object with a ruler which has millimeter marks, you might find it is actually 1cm long (or thick) with a millimeter accuracy. You can then write the result as $10,\text{mm}$ or $1.0,\text{cm}$ or $0.010,\text{m}$ and those trailing zeros are significant, because they carry a valuable information about the measurement precision (1m is, rougly speaking, 'about one meter', 1.000m is 'one meter precise to below 1mm'). – CiaPan Jul 07 '15 at 20:28
  • That's why a 'scientific notation' is popular in science, engineering and physics: you can't write the Earth mass is 5972190000000000000000000 kilograms, because it would make a false precision, but you can write it is 5.97219e24 kg, which denotes the same value, but also specifies its accuracy. (Ping @AndréNicolas) – CiaPan Jul 07 '15 at 20:35

1 Answers1

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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:

AlannaRose
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