Chemistry depends on measured masses, volumes and temperatures. Each value is a number with a unit, and has only as many significant figures as the instrument can resolve. Precision and accuracy are different things.
In a laboratory you weigh solids, measure volumes of liquids and record temperatures. Each result is a number with a unit: 5 g, 250 mL, 25 °C. Without the unit, the number does not say what was counted.
Chemists use the SI system, which has seven base units. Mass is in kilograms, length in metres and time in seconds. In the laboratory, smaller units are more convenient: the gram (10⁻³ kg) and the millilitre (10⁻⁶ m³, the same as 1 cm³). The SI unit of amount of substance is the mole, the subject of the next sessions.
Chemistry deals with very large and very small numbers. 2 g of hydrogen gas contains about 602,200,000,000,000,000,000,000 molecules. One hydrogen atom has a mass of about 0.00000000000000000000000167 g.
In scientific notation, a number is written as a value from 1 up to 10, multiplied by a power of ten. The two numbers become 6.022 × 10²³ and 1.67 × 10⁻²⁴ g. Scientific notation is shorter, and it also shows the number of significant figures without ambiguity.
A rough balance might read 9.4 g for an object. An analytical balance might read 9.4213 g for the same object. The second balance resolves smaller differences in mass.
The significant figures of a measurement are the digits known reliably, plus the first estimated digit. 9.4 g has two; 9.4213 g has five. Writing more digits than the instrument resolved claims a precision the measurement does not have.
Rules for counting them:
A mass is recorded as 0.0250 g. How many significant figures does it have? Which zeros count and which do not?
Three: the 2, the 5 and the final 0.
The two leading zeros only place the decimal point. Written as 2.50 × 10⁻² g, they disappear. The trailing zero after the 5 is significant because there is a decimal point. It states that the balance read 0.0250, not 0.0249 or 0.0251.
100, written without a decimal point, could be known to one figure or to three. By convention it is counted as one significant figure. Writing 100. shows three. Writing 1.00 × 10² also shows three, without ambiguity.
Precision is how close repeated measurements are to one another. Accuracy is how close a measurement is to the true value. A set of measurements can have one without the other.
Suppose the true mass is 2.00 g. Readings of 1.95 g and 1.93 g are precise, because they agree closely, but not accurate, because both are about 0.06 g low. Readings of 1.94 g and 2.05 g are neither. Readings of 2.01 g and 1.99 g are both precise and accurate.
A faulty balance always reads 0.5 g too high, and gives nearly the same reading every time. Are its readings precise, accurate, both, or neither?
Precise but not accurate. The readings agree closely with each other, so they are precise.
They all differ from the true value by 0.5 g, so they are not accurate. An error that is the same every time is called a systematic error. Repeating the measurement does not reveal it; checking the balance against a known standard mass does.
Keep extra digits during the working and round only the final answer, so rounding errors do not accumulate.
1How many significant figures are in 0.0250 g? Answer: ____.
2By convention, how many significant figures does 100 (no decimal point) have?
3A balance always reads 0.5 g too high, and its readings agree closely. They are…
42.5 × 1.25 = 3.125 on a calculator. Correctly reported, it is…
512.11 + 18.0 + 1.012 = 31.122. Correctly reported, it is…
6Why are measured values often written in scientific notation?
Next: the laws that describe how elements combine.
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