Improving your measuring

Precision and uncertainty

Try to be more precise in your measuring. Use an instrument with a smaller resolution, and read it to the smallest reading possible.

Two rulers. Ruler A measures to the nearest milimeter. Ruler B measures to the nearest centimeter.

Ruler A will give a more precise reading and will reduce the uncertainty in your result.

An uncertainty of 1 mm in 25 mm is 4 %.

An uncertainty of 1 cm in 2.5 cm is 40 %. This is ten times bigger.

How is uncertainty calculated?

{\%{\text{~uncertainty in reading}}}=\frac{\text{instrument resolution}\times 100\%}{\text{reading taken}}

The resolution is the smallest division on the instrument.

Question

What is the uncertainty of a resolution of 0.01 ml in 5.52 ml?

(0.01 ÷ 5.52) × 100 % = 0.18 %

Question

What is the uncertainty of a resolution of 0.5 ml in 5.5 ml?

(0.5 ÷ 5.5) × 100 % = 9.1 %

curriculum-key-fact
To make the uncertainty small, use a highly precise instrument with a small resolution and measure a large reading.