Write 7 576 767 000 s to two significant figures in scientific notation and with a prefix.
7.58 x 10^9 s (7.58 Gs)
7 600 000 000 s is the rounded value to two significant figures.
Write 0.003789 s to two significant figures in scientific notation and with a prefix.
3.79 x 10^-3 s (3.79 ms)
Rounded to two significant figures.
Calculate the average speed of a journey of 869 m which takes 15 s.
58 ms^-1
Average speed is calculated as v = d/t = 869/15.
What are the three main types of uncertainty?
- Systematic uncertainty
- Scale reading uncertainty
- Random uncertainty
What causes systematic uncertainty?
A constant factor affecting all measurements in the same way
Examples include scale not set to zero or measuring tape stretched.
How is scale reading uncertainty calculated for analogue scales?
± ½ the least division
For example, if the smallest division is 0.1 cm, the uncertainty is ± 0.05 cm.
How is scale reading uncertainty calculated for digital scales?
± 1 in the least significant digit.
What does random uncertainty measure?
The spread of measurements
The wider the spread, the less precise the measurement.
What is the formula to calculate random uncertainty?
Random uncertainty = (max. – min.) / number of readings.
What is the relationship between accuracy and precision?
- Accuracy: Closeness to the ‘true’ value
- Precision: Smallness of uncertainty
How is absolute uncertainty represented?
As (measurement ± uncertainty)
Example: (12 ± 0.7) cm.
What is the formula for percentage uncertainty?
% Δ = (uncertainty / reading) x 100.
What is the process to compare and combine uncertainties?
Calculate percentage uncertainty for each measurement, then use the larger % uncertainty for the final result.
What indicates a direct proportion between two variables?
A graph of Y against X is a straight line through the origin.
What indicates an inverse proportion between two variables?
A graph of Y against 1/X is a straight line through the origin.
What is an example of a systematic uncertainty?
A scale that consistently reads too heavy.
How do you express a measurement with uncertainty?
Use brackets around the measurement value and the uncertainty value.
What is the final absolute uncertainty based on percentage uncertainty?
The larger % uncertainty is the uncertainty of the final result.
What is the significance of the mean value in measurements?
It gives the best estimate of the true value.
What does a precise measurement indicate?
Small uncertainty and consistency in results.
What is the formula for calculating speed?
v = d / t.
How is the average speed expressed with uncertainty?
As speed ± percentage uncertainty.
What is the meaning of ‘g = (9.8 ± 0.3) ms^-2’?
g lies between 9.5 and 10.1 ms^-2.
What does ‘g = (9.62 ± 0.01) ms^-2’ signify?
g lies between 9.61 and 9.63 ms^-2.
