How to Interpret Scale Readings in Measurement

Instructor: Matthew Bergstresser

Matthew has a Master of Arts degree in Physics Education

Measurements are a part of gathering data in science and in medicine. Being able to interpret the scales of a variety of measuring devices is critical in getting correct values. This lesson will outline how to interpret scale readings from a variety of measuring instruments.

Measurement

In the average day of the average person, how many measurements are taken? Taking myself as an example, I will tell you the measurements I took yesterday.

I decided to make peanut brittle. I needed to weigh sugar on a scale, measure water in a measuring cup, take the temperature of the mixture with a thermometer, and measure the length and width of a baking sheet. Measurements are taken everywhere, from kitchens to hospitals and everywhere in between! Let's look at how to read measurements.

Scale

A scale on a measuring device comprise the markings that indicate a certain amount of whatever is being measured. The number of marks on a measurement device relay how precise a measurement can be. The more marks, the more precise. We divide the difference between successively numbered values by the number of spaces between them. Diagram 1 shows there is a difference of 1 between the successively numbered values and there are 10 spaces between them. 1/10 is 0.1, therefore each smaller mark represents 1/10 (0.1) of the distance to the next larger number. Measurements with this device can be precise to 2 decimal places. We can add a last digit which is estimated.


marks_spaces

Example 1:

Prompt: Determine the length of the red line to 2 decimal places.


ex1

Solution: The red line goes just past 1.3, but not quite to 1.4. We can estimate the second decimal place. It looks like the line goes roughly halfway between 1.3 and 1.4, so we will say it's 1.35.

The next ruler has a difference of 1 between the successively numbered values and 20 spaces between them. 1/20 (0.05) is the distance between each little mark. Making a measurement with this device is more precise compared to the previous ruler. We can report a value to 3 decimal places.


20_spaces

Example 2:

Prompt: Determine the length of the red line to 3 decimal places.


example2

Solution: The line goes past 1.05, but is short of 1.1. We can estimate the third decimal place, giving us a final answer of 1.054.

Units

A unit is a standard being measured. For example, a common unit of length is the foot in the Imperial system, and the meter in the SI (metric) system. These examples are also called pure units because there is nothing that makes up the unit. A foot or a meter is just a length. A derived unit is a unit in which other multiple units are combined, giving physical meaning to the measurement. For example, speed is measured in meters per second (m/s).

Reporting incorrect units with a measurement varies in severity from a baked food item tasting horrible to a medical emergency due to the wrong dosage of medicine administered.

Let's look at a thermometer.


thermometer

What is the reading on the thermometer? We know how to deal with the scale of the thermometer, but why is there a range of numbers on either side? The left side represents degrees in Celsius (SI system) and the right side represents degrees in Fahrenheit (Imperial system). I know this because water freezes at 32o F, which corresponds to 0o C. Let's determine the reading on the thermometer in both systems starting with Celsius. A red dotted line has been drawn where we need to take the reading.


closeup

There are 10 degrees between the successively numbered values on the Celsius side with 10 spaces between them. 10/10 is 1, therefore each little line is 1o C. The red dotted line is just past 21 and we can estimate 1 digit, giving us a final reading of 21.1o C.

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