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Record measurements and compare instruments

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Instrument A displays steps of 0.001 mL but has a stated maximum error of ±0.3 mL. Instrument B displays steps of 0.01 mL with a stated maximum error of ±0.03 mL. Which has the tighter accuracy specification?

Year 9, Chapter 6, 4 difficulty levels, Calculator allowedBuild a worksheet

Measurement specifications and records

A measurement record should reflect the stated procedure and instrument specifications. Written precision is not a substitute for calibration

  1. Resolution The smallest displayed or marked change is the resolution. More displayed digits do not by themselves prove accuracy
  2. Accuracy specification Compare stated maximum errors under the same conditions. A smaller maximum error gives a tighter guarantee; calibration still matters
  3. Range and suitability An instrument must cover the required quantity and meet the allowed error. A precise-looking result outside the range is not supported
  4. Written precision Follow the stated recording increment. In scientific notation, retain zeros in the coefficient when they state significant figures \(\displaystyle 12.0\text{ mL}=1.20\times10^1\text{ mL}\)

Worked example

A laboratory record gives 0.00620 g to three significant figures. Rewrite it in scientific notation without changing its value or written precision

\[0.00620\text{ g}\]
  1. \(\displaystyle 0.00620=6.20\times10^{-3}\)Move the decimal point three places right and use exponent −3.
  2. \(\displaystyle 6.20\times10^{-3}\text{ g}\)The final zero preserves the three significant figures in the original record

Common mistakes

Equating resolution with accuracy
✕\(\displaystyle \text{A must be more accurate}\)✓\(\displaystyle \text{B has the smaller error limit}\)
For A, suppose the display step is 0.001 mL and the maximum error is ±0.3 mL. For B, the step is 0.01 mL and maximum error is ±0.03 mL. A has finer resolution, but B has the tighter accuracy specification
Dropping recorded precision
✕\(\displaystyle 4.5\times10^{-3}\quad(3\text{ s.f.})\)✓\(\displaystyle 4.50\times10^{-3}\quad(3\text{ s.f.})\)
The values are equal, but 4.5 has only two significant figures. Keep 4.50 to preserve the three significant figures in 0.00450 g.

Difficulty levels

introRound a calculated mass or volume to a supplied reporting increment
standardEnter a scientific coefficient and exponent while preserving three significant figures
challengeCompare maximum-error specifications and check both range and error requirements
examSelect normalised scientific notation with the same value and written precision

Questions about this topic

Does adding zeros improve an instrument?+

No. Extra written digits do not improve calibration, resolution or accuracy

Should every analogue reading have one estimated digit?+

Follow the specified procedure. Whether to estimate between graduations depends on the instrument and conditions; do not apply one extra-digit rule to every instrument

What if neither instrument meets the requirement?+

Choose another suitable instrument or revise the procedure with justified uncertainty. Do not claim that an unsuitable measurement meets the stated requirement

Can I use a calculator?+

A calculator is allowed unless a question is marked no calculator

Which year level and chapter is this?+

Year 9 Mathematics, chapter 6: Indices and surds

In this chapter

Work with index notationExpress a number in prime-factor index formSimplify using index laws 1 and 2Simplify using index law 3 and the zero powerExpand using index laws 4 and 5Work with negative indicesSolve an exponential equation by matching basesCombine positive and negative integer indicesScientific notationMultiply and divide in scientific notationSI prefixes and scientific timescalesRound to decimal places and significant figuresRecord measurements and compare instrumentsRelate fractional indices to roots (optional extension)Locate exact square roots on the real number lineSimplify, compare and operate with surds (optional practice)