Measuring, Precision vs. Accuracy, and Intro to Significant Figures

What do we measure? Volume – the amount of space taken up by a substance Mass – the amount of matter in an object Temperature – measure of how much thermal energy a substance has compared to a reference point Length – straight line distance between 2 points

What do you measure with?

Units of Measurement You cannot just record a number for a measurement. A unit must also be indicated. For example, a measurement is taken for the length of the laboratory table and recorded as 183 is not correct. A correct recording would be 183 centimeters (cm). All measurements should be made in metric units, or converted to metric.

Measuring Liquids – Volume! When you measure the volume of a liquid it is important to make sure that you use the appropriate kind and size of instrument. When you put a sample of a liquid into one of these instruments you will notice a curve at the surface of the liquid. This curve, which is called a meniscus. Adjust your body and head so that you are eye level with the instrument and the meniscus. Read the volume of the liquid at the bottom of the meniscus.

The triple beam balance Measuring Mass The triple beam balance Carrying the Balance Be sure all movable masses are back to the zero point. Place one hand under the balance and the other hand on the support (arm) to carry the balance. Using the Balance Zero the balance before you determine the mass of any substance.         a) Slide all of the movable masses back to the zero point.         b) Check to see that the pointer swings freely along the scale.       

Mass cont. Never put a hot object directly on the balance pan. Any dry chemical that is to be massed should be placed on paper or in a container. Never pour chemicals directly on the balance pan. Remember to mass the paper or container before adding the substance. Once you have placed the object to be massed on the pan, move the riders along the beams beginning with the largest mass first. If the beams are notched, make sure all riders are in a notch before you take a reading.

What is the mass?

Answer!

Measuring Temperature We will use degrees Celsius in this class! Never stir with a thermometer. Never read a temperature with a thermometer leaning against a side of a beaker. NO WAY! ->

Measuring Length Meter sticks are carefully calibrated in centimeters with a millimeter least count. That is, the millimeter is the smallest subdivision on the meter stick. This means the millimeter is the unit of the smallest reading that can be made without estimating.

Figure 2. An example of a meter stick reading Figure 2. An example of a meter stick reading. The object's length is measured to be 41.64 cm. (See text for description.) Figure 1. This meter stick is calibrated in centimeters (shown as the numbered major divisions) with a least count of millimeters.

Reading instruments to significant figures The least count of this meter stick is one millimeter, so we know with absolute certainty that the object is between 41.6 cm and 41.7 cm. We then estimate the object's length to the fractional part (doubtful figure) of the least count subdivision… 41.64 cm.

Let’s do this again…What is the mass?

Answer = 216.49 cm

Sig Figs Significant digits or significant figures are digits read from the measuring instrument plus one doubtful digit estimated by the observer. Examples: 203.4 cm: least count of ruler was 1 cm, tenth of centimeter was estimated. 4.07 cm: least count was 0.1 cm. hundredth of centimeter was estimated.

Rules for Sig Figs Digits from 1-9 are always significant. Zeros between non-zeros are always significant Zeros at the beginning of a number are never significant, they merely indicate the position of the decimal point Zeros that fall both at the end of the number AND after the decimal point are always significant When a number ends in zeros but contains NO decimal point the zeros may or may not be significant….if this is the case, we use scientific notation!

Examples EXAMPLES # OF SIG. DIG. COMMENT 453 kg 3 All non-zero digits are always significant. 2004 L 4 Zeros between 2 sig. dig. are significant. 5.00 Additional zeros to the right of decimal and a sig. dig. are significant. 0.007 1 Placeholders are not

Practice problems What is the number of sig figs in each of the following: 1282 kg 0.00296 s 8.070 mm 0.0105 L 9.7750 x 10-4 m

Accuracy and Precision Accuracy-the closeness of a measurement is to the true value of what is measured Precision- a gauge of how exact a measurement is Which is more precise…a glug ruler or a 0.01 glug ruler? Why? With which ruler can you report more significant figures?

Accuracy vs. Precision

Clock Example Digital vs. analog