When reporting a measurement, how many significant digits should I use? PreLab 1.6

BIOL 1406

PreLab 1.6

When reporting a measurement, how many significant digits should I use?

When making measurements, you must report your results using the correct number of significant digits (also called significant figures.) The significance of a digit has to do with whether or not it represents a true measurement. Any digit that can be accurately measured or reasonably estimated with the particular measuring device you are using is considered significant.

It is easy to determine the number of significant digits when using a digital measuring device; simply assume that all digits shown on the display are significant. For example, if you are weighing an object on an electronic balance and the display shows 93.14 g, record all of the digits and assume that the balance can accurately estimate the weight to the nearest one-hundredth of a gram. In this case there are 4 significant digits.

Balance reading with 4 significant digits

When using an analog measuring device, the decision is a little more complicated. In this case, the first estimated digit should be the last significant digit reported in the measured value. For example if you are measuring temperature with a thermometer where the smallest calibration marks are 10 degrees apart, then the first estimated digit would be the nearest whole degree and that would be the last significant digit reported in your value. Such a thermometer could be used to report a temperature of 47 ^oC but not 47.0 ^oC or 47.00 ^oC. On the other hand, if the smallest calibration marks on the thermometer are one degree apart, then the first estimated digit would be tenths of a degree and that should be the last significant digit reported in your value. Such a thermometer could be used to report a temperature of 47.0 ^oC but not 47 ^oC or 47.00 ^oC.

Look at the thermometer on the right, notice that the marks are in 10 degree increments. On this device, the most accurate measurement would be plus or minus 1 degree. Therefore, the value should be read as 35 ^oC, not 35.0 ^oC.

Thermometer

Notice that on the top scale, we can approximate the distance more accurately, i.e. 3 significant digits, compared to the same distance measured using the bottom scale, i.e. 2 significant digits.

Your Turn
Look carefully at the picture below. Enter you answers in the space provided, then check and see how you did. Mouse over the links below to check your answer.

What is the length of the gray object? Don't forget the units!	Check your answer.
How many significant digits does the measurement have?	Check your answer.
Mouse over for more information.

How do I determine the number of significant digits in a reported measurement?

To determine the number of significant digits in a reported measurement, we need to look at two cases:

A. Numbers with Indicated Decimals

1. All non-zero digits (1-9) are counted as significant.

2. Only zeros that have non-zero digits somewhere to the LEFT of them are considered significant – all other zeros are place holders

For example, in the value 0.0012010 g, only the last 2 zeros have non-zero digits to their left and are counted as significant. The first 3 zeros are merely place holders and are not significant digits. Therefore, the total number of significant digits in this value is 5.

B. Numbers without Indicated Decimals

1. All non-zero digits (1-9) are counted as significant.

2. Zeros that have non-zero digits somewhere to the RIGHT of them are considered significant, but there is no way of knowing whether any other zeros are significant.

For example, in the value 100,500 g, the first 2 zeros are significant because there is a non-zero digit to their right. However, we really don’t know if the 3^rd or 4^th zeros are significant. This ambiguity can be avoided by writing the number with a decimal or by using scientific notation. When using scientific notation, all digits before the multiplication sign are considered significant. For example, to write 100,500 g using scientific notation:

If the 3^rd and 4^th zeros are not significant, you could write 100.5 x 10³ g (4 significant digits)
If the 3^rd zero is significant but not the fourth, you could write 100.50 x 10³ g (5 significant digits)
If both the 3^rd and 4^th zeros are significant, you could write 100.500 x 10³ g (6 significant digits)

Your Turn
You are measuring the migration distance of protein bands in a gel using a ruler where the smallest calibration marks are 1 mm apart. For each of the following recorded measurements type in "yes" if it has the correct number of significant digits and type in "no" if it does not.
23 mm	Hint	Check your answer.
23.0 mm	Hint	Check your answer.
2.3 cm	Hint	Check your answer.
2.333 cm	Hint	Check your answer.
2.34 cm	Hint	Check your answer.
23.64 mm	Hint	Check your answer.
0.0231 m	Hint	Check your answer.
Write down the number of significant digits in each of the following recorded measurements.
23.0167 g	Hint	Check your answer.
0.0034 g	Hint	Check your answer.
45.0021 g	Hint	Check your answer.
104.50 g	Hint	Check your answer.
0.0010 g	Hint	Check your answer.
3.00 x 10⁴ g	Hint	Check your answer.

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