# Question #0710f

##### 1 Answer

The answer is **(c)**

#### Explanation:

So, you use a vernier caliper with a *least count* of

You measure the wire to have a thickness of *least count* of the vernier calipers.

The absolute uncertainty of the instrument is actually equal to **half** of the least count, which in this case would be

#"abs. uncertainty" = "0.01 cm"/2 = +- "0.005 cm"#

However, you need to report this uncertainty using the **same number of decimal places as the measurement**. In your example, the measurement is rounded to the *hundredths place*, shown here in red

#0.4color(red)(5)#

This means that you need to round the uncertainty to the *hundredths place* as well, which in your case would be

#+- "0.005 cm" ~~ +- 0.0color(red)(1)color(white)(x)"cm"#

In this respect, you always need to report the absolute uncertainty to the **same decimal place** as the measurement.

The **percentage uncertainty** can be calculated using the absolute uncertainty and the actual measurement

#"% uncertainty" = "absolute uncertainty"/"measured value" xx 100#

In your case, the percentage uncertainty will be equal to

#"% uncertainty" = (0.01color(red)(cancel(color(black)("cm"))))/(0.45color(red)(cancel(color(black)("cm")))) xx 100 = 2.222%#

You can only use two sig figs for the answer, so you have

#"% uncertainty" = color(green)(2.0%)#

For two measurements, keep in mind that the measurement that has the **smaller** absolute uncertainty is more **precise**, and that the one that has the **smallesr** percent uncertainty is more **accurate**.