Recording Information Significantly

When YOU are the measurer, it is important to learn how to record the measured value significantly. Every piece of measuring equipment has a precision that is inherent in the manufacture of the device. You need to record the measurement so that the number you record reflects the precision of the instrument.

The rule is to record all divisions marked on the piece of equipment and one estimated digit. The graduated cylinder at the right is divided into the units' place. Therefore, a measurement made with this piece of equipment would be recorded to the tenths place which would be estimated.

This sample is mercury and the meniscus(level of the liquid)is convex. The volume is read at the top of a convex meniscus. Water and water solutions will have a concave meniscus. The volume is read at the bottom of the meniscus.

Using Measured Values in Calculations

Learning to correctly report an answer for a calculation that has involved measured values must reflect the precision of the equipment used to make the measurements. It is the responsibility of the person reporting the calculated value to convey information as to how many of the digits in the answer are meaningful, given the devices used to make the measurements. In other words, the student must decide how many of the digits in the answer are meaningful. One method for doing this is the use of Significant Figure Rules.

Rule 1 For Division and Multiplication

In division and multiplication calculations keep only the number of digits(Count the digits!)in the answer equal to the least number of digits in either of the values in the multiplication or division.

Example 1: A student determined the mass of an object to be 2.430 grams and that the object occupied 3.5 mL of volume. Determine the density of the material.

Example 2: Another student determined the mass of a liquid on a more expensive balance. The mass was 4.7302 grams and the volume was determined to be 3.200 mL What is the density of the liquid?

Example 1

Density = mass/volume

Density = 2.430 grams/3.5 mL

Density = 0.69g/ml

Example 2

Density = mass/volume

Density = 4.7302 grams/3.200mL

Density = 1.322 g/mL

Rule 2 For Addition and Subtraction

In addition and subtraction calculations round off the answer to the same decimal place as the least precise value in the values being added or subtracted. (Watch the decimal place!)

Example 3: A student determines the mass of a sample of silver on an analytical balance to be 14.236 grams. Another student has some silver and uses a less expensive balance that records the mass to only two decimal places. He finds the mass of that sample to be 175.22 grams. What is the total mass of silver?

The two masses of the two samples are added: