Sig Figs: 10.00cm, 16.38cm, 29.10cm to 2 Decimal Places

[physicslady123]

Homework Statement

I am doing a lab and the measurements I took are from a meter stick. It should be to 2 decimal places (e.g. 10.00cm, 16.38cm, 29.10cm). For my calculations, I need to put the data into meters. As a result, would it be to 4 digits after the decimal?

Relevant Equations

Significant Figures

e.g. 10.00cm = 0.0010 m, 16.38cm = 0.1638 m, 29.10 cm = 0.2910 m

Or, would the sig figs for the meters be to 2 digits after the decimal (e.g. 16.38 cm = 0.16 m)

 

[haruspex]

the measurements I took are from a meter stick. It should be to 2 decimal places

Specifying two decimal places is meaningless without also specifying the units.
If the specified units are cm, 2 decimal places seems remarkably precise for reading off a meter stick.
Are you sure it does not specify two significant figures?

 

[Cutter Ketch]

We can have a different discussion about whether your measurement really was precise enough to write four significant figures.

Taking that as a given, when you convert your data, it should retain the same number of significant digits as it had in the original unit. 29.10 cm becomes 0.2910 m both of which have four significant digits. After all, you didn’t lose any information just changing units.

This can be tricky going the other way. For example 2.00 m becomes 200 cm, but those zeros are significant. You must show that they aren’t just place holders and also count them as significant digits in subsequent calculations. You show that they are significant by putting a bar over the last significant zero.

 

[haruspex]

Another thought...
You need to be careful if you take a difference of two such measurements. If you have 29.10 and 32.07 then the difference is 2.97. You cannot argue for still having four significant figures, as in 2.970.