Chromatography: provide answers to an appropriate number of significant figures.

The idea

In chromatography, measured distances and calculated R_f values must be reported with a sensible number of significant figures. The number of significant figures is the count of meaningful digits in a value, starting from the first non-zero digit; for example, 4.62 cm has three significant figures, and 0.0580 has three because the zeros after the 5 and 8 are significant. When you measure a solvent front of 8.0 cm and a spot distance of 3.2 cm, the R_f is 3.2 ÷ 8.0 = 0.40, which is appropriately given to two significant figures, matching the precision of the measurements. Do not overstate precision by writing many digits from a calculator display, and do not round so heavily that the value becomes misleading. The appropriate number depends on the precision of the measurements and the context of the calculation.

What earns the marks

• State that significant figures are the meaningful digits in a measured or calculated value, counted from the first non-zero digit.
• Apply the rule that leading zeros are never significant, while zeros between non-zero digits and trailing zeros after a decimal point are significant.
• Calculate R_f as the distance travelled by the substance divided by the distance travelled by the solvent front, then round the result to a sensible number of significant figures.
• Match the number of significant figures in a reported answer to the precision of the measurements, avoiding excessive digits copied from a calculator.
• Recognise that a value such as 0.40 has two significant figures, whereas 0.4 has one, and choose the form that reflects the measurement precision.

Common mistakes and how to put them right

• Counting leading zeros as significant, for example treating 0.058 as having five significant figures.

  Put it right by starting the count at the first non-zero digit, giving two significant figures.

• Copying every digit from a calculator display, such as writing an R_f of 0.3970588.

  Put it right by rounding to a sensible number of significant figures, for example 0.40.

• Confusing significant figures with decimal places, for example giving 0.40 as two decimal places rather than two significant figures.

  Put it right by identifying the first significant digit and counting from there.

Exam tips

• Write down the measured distances with their units before dividing, so the significant figures in the final R_f value are easy to justify.
• Check whether the question asks for significant figures rather than decimal places, and count digits from the first non-zero digit.
• If a calculated R_f is exactly 0.4, consider whether reporting 0.40 better reflects the precision of measurements such as 3.2 cm and 8.0 cm.