Significant figures and uncertainty

When asked to estimate the number of steps required to walk the length of the Appalachian Trail,

Joe said
```
            2,589,842
  
```
Pamela said
```
            2,100,000
  
```

Which student's answer is more sensible? Why?

Scientists pay careful attention to the way they write numerical values. They use only as many digits as they can justify, a practice we describe as providing only the significant digits. There is a connection between the number of significant digits in a written quantity and the uncertainty in that quantity.

One significant digits corresponds roughly to an uncertainty of around 20 to 50 percent
```
            2,000,000     8 x 10^(22)      0.03
  
```
Two significant digits corresponds roughly to an uncertainty of around 2 to 5 percent
```
            2,100,000   8.9 x 10^(22)      0.030
  
```

Can you explain the mathematical basis for this connection?

Significant figures are like viruses: they infect any numbers they touch. If you combine two quantities, one with 5 significant figures and another with 1, then the result will have only 1 significant figure.

How many significant digits should you be using in your estimates of the number of strides?

You can read more about significant figures in Section 1-10 of your textbook, and in Appendix A part 5.