For all measurements estimate the next significant figure. For example, say the writing utensil has a length that falls between 1 dm and 2 dm. Estimate the length to the nearest 0.1 dm. When measuring using centimeters estimate to the nearest 0.1 cm. Finally, measure the writing utensil to the nearest 0.1 mm.
Take the black line below as an example. Look at the top ruler and estimate how long it is in decimeters. I get a value of about 0.5 dm. Now look at the middle ruler. It’s clear that the end of the line is between 5 cm and 6 cm so I estimate that its length is about 5.5 cm. Now, looking at the bottom ruler I can see that the line’s length is between 55 and 56 mm. So I estimate that the line has a length of 55.5 mm (5.55 cm or 0.555 dm).
Because I estimated the last digit there is some uncertainty in it: all the digits but the last are precise but the last one was estimated. If I did a good job then that value might range plus 1 or minus 1 (± 1).
Length in dm | Example: 1.4 ± 0.1 dm | |
Length in cm | Example: 14.2 ± 0.1 cm | |
Length in mm | Example: 142.3 ± 0.1 mm |
At the front of the room there are three graduated cylinders. These instruments are used to measure out approximate volumes of fluids and can be read to a fairly high level of precision. The smaller the cylinder, the better the precision. Here is how to read the volume in a graduated cylinder to the highest possible precision. First, you read the volume using the meniscus. The meniscus is the curved upper surface of a fluid in a narrow tube. With water the meniscus curves downward. Read the volume using the lowest part of the meniscus as shown in the illustration with the dotted line. In the illustration the volume is between 9.7 mL and 9.8 mL and you can estimate here to 0.1 mL since marks are given every 1 mL. Doing so gives a volume of 9.76 mL. Note: In general you can estimate to a precision of ^{1}/_{10} (0.1) the size of the smallest division on a measuring instrument. When you measure the volumes in the cylinders always estimate the volume to ^{1}/_{10} the size of the smallest division.
Vol. in the 1 L cylinder | Example: 451 ± 1 mL | |
Vol. in the 100 mL cylinder | Example: 82.4 ± 0.1 mL | |
Vol. in the 10 mL cylinder | Example: 5.68 ± 0.01 mL |
There are three objects at the front of the room that your teacher has set out for you to weigh. Lab balances have limits on their precision just like rulers and graduated cylinders. Just because the balance gives a digital readout doesn’t mean that the last digit is as certain as the others. Think of the last digit as the estimated digit. The last digit is the first uncertain digit. The triple-beam balances achieve a higher precision based on your estimation of the last digit, just as for the linear measurements using the ruler.
Using 3-Beam Balance | Using Digital Balance | |
Mass of ____________________ | ± ______ | ± ______ |
Mass of ____________________ | ± ______ | ± ______ |
Mass of ____________________ | ± ______ | ± ______ |
Now we will move back to length measurements. Using a short ruler (not a meterstick), measure the length and width of the lab bench. Next, use a meterstick. For both measurements, report your answer in centimeters.
Using a Short Ruler | Using a Meterstick | |
Length | ± ______ | ± ______ |
Width | ± ______ | ± ______ |