Uncertainty

What is uncertainty?

A reading when using a particular instrument is no smaller than plus or minus half of the smallest division or grater. E.g a temperature measured with a thermometer is likely to have an uncertainty of +-0.5C if the graduations at 1C apart

What is the uncertainty of a reading (one judgment)?

At least +-0.5 of the smallest scale reading

What is the uncertainty of a measurement (two judgments)?

Atleast +-1 of the smallest scale reading

A measuring cylinder is divided into 10cm3 graduations. Each 10cm3 further divided into 1cm3. What is my uncertainty?

0.5cm3

A 10cm3 pipette has 1cm3 division. Each 1cm3 had 10 subdivision. What is the uncertainty of volume using the pipette?

0.05cm3

A ruler is divided into mm. What is the uncertainty of any measurement?

0.5mm x 2 = 0.1mm

As two measurement judgements, each time the ruler is used

What is the equation for percentage uncertainty (in a measurement)?

Percentage uncertainty = uncertainty/ value x 100

What is the equation for percentage uncertainty (in a repeated measurement)?

Percentage uncertainty = uncertainty / mean value x 100

I use a 10cm3 peppers to measure 10cm3 water. Smallest graduations = 0.1cm3. What is the % error?

0.05/10 × 100 = 0.5%

U use a 100cm3 measuring cylinder to measure 10cm3 water. Smallest graduations = 1cm3. What is the % error?

0.5/10 × 100 = 5%

I use a 1cm3 pipette (with 0.01cm3 graduations) to measure 10cm3. What is the % error?

0.005-1 × 100 = 0.5 × 10 = 5%

What to do when multiplying values?

Add the percentage uncertainties

What to do when dividing values?

Add the percentage uncertainties

What to do with power rules?

Multiple the percentage uncertainty by the power