What is the significance of precision and accuracy

Reproducibility : The variation observed when different operators measure the same part using the same device. A dart board can help us visualize the difference between the two concepts:. Accurate and Precise Precise Accurate, but not Precise Neither Accurate nor Precise.

Maybe this example can help to further show the differences. You test the weight of the bags using a scale that measures the bags precisely in other words, there is little variation in the measurements , but not accurately — measuring SI units include meters m for length, liters L for volume, kilograms kg for mass, seconds s for time, Kelvin K for temperature, ampere A for electrical current, mole mol for amount and candela cd for luminous intensity.

When taking scientific measurements, it is important to be both accurate and precise. Accuracy represents how close a measurement comes to its true value. This is important because bad equipment, poor data processing or human error can lead to inaccurate results that are not very close to the truth. Precision is how close a series of measurements of the same thing are to each other. Measurements that are imprecise do not properly identify random errors and can yield a widespread result.

Measurements are only as accurate as the limitations of the measuring instrument allow. For example, a ruler marked in millimeters is accurate only up to the millimeter because that is the smallest unit available.

When making a measurement, its accuracy must be preserved. This is achieved through "significant figures. The significant figures in a measurement are all the known digits plus the first uncertain digits. For example, a meter stick delineated in millimeters can measure something to be accurate to the fourth decimal place. A grocery store sells a 5-pound bags of apples.

You purchase four bags over the course of a month and weigh the apples each time. You obtain the following measurements:.

We can use the following equation to determine the percent uncertainty of the weight:. Consider how this percent uncertainty would change if the bag of apples were half as heavy, but the uncertainty in the weight remained the same. If you do not do this, you will have a decimal quantity, not a percent value.

There is an uncertainty in anything calculated from measured quantities. For example, the area of a floor calculated from measurements of its length and width has an uncertainty because the length and width have uncertainties. How big is the uncertainty in something you calculate by multiplication or division?

If the measurements going into the calculation have small uncertainties a few percent or less , then the method of adding percents can be used for multiplication or division. This method says that the percent uncertainty in a quantity calculated by multiplication or division is the sum of the percent uncertainties in the items used to make the calculation. For example, if a floor has a length of 4. Expressed as an area this is 0.

A high school track coach has just purchased a new stopwatch. Why or why not? An important factor in the accuracy and precision of measurements involves the precision of the measuring tool.

In general, a precise measuring tool is one that can measure values in very small increments. For example, a standard ruler can measure length to the nearest millimeter, while a caliper can measure length to the nearest 0.

The caliper is a more precise measuring tool because it can measure extremely small differences in length. The more precise the measuring tool, the more precise and accurate the measurements can be. When we express measured values, we can only list as many digits as we initially measured with our measuring tool.

For example, if you use a standard ruler to measure the length of a stick, you may measure it to be You could not express this value as It should be noted that the last digit in a measured value has been estimated in some way by the person performing the measurement. For example, the person measuring the length of a stick with a ruler notices that the stick length seems to be somewhere in between Using the method of significant figures, the rule is that the last digit written down in a measurement is the first digit with some uncertainty.

In order to determine the number of significant digits in a value, start with the first measured value at the left and count the number of digits through the last digit written on the right. For example, the measured value Significant figures indicate the precision of a measuring tool that was used to measure a value. Special consideration is given to zeros when counting significant figures. The zeros in 0. There are two significant figures in 0. The zeros in The zeros in may or may not be significant depending on the style of writing numbers.

They could mean the number is known to the last digit, or they could be placekeepers. So could have two, three, or four significant figures. To avoid this ambiguity, write in scientific notation. Zeros are significant except when they serve only as placekeepers. Determine the number of significant figures in the following measurements:. Another group of students used Vernier calipers to take the measurements. They were able to measure to a tenth of a millimeter. If several measurements are made with a more precise instrument, such as calipers, then the average value can be considered a more accurate value than the one taken with a ruler.

Precision refers to how close measured values are to each other. For example, one group of students Group A counted the number of tomatoes on their tomato plant, while another group of students Group B did the same for the tomatoes on their tomato plant. Notice that the all of the values for Group A are very similar either 36 or The data would be considered to be very precise. On the other hand, the values for Group B show a much larger range between 31 and These measurements are not precise.

Student responses: 53 cm 2 , 52 cm 2 , 53 cm 2 , 53 cm 2.