Measurements and their errors

Question 1

Random error

Answer 1

Measurements vary due to unpredictable circumstances. They can’t be corrected and can only be mitigated by making more measurements and calculating a new mean.

Question 2

Systematic error

Answer 2

Measurements differ from the true value by a consistent amount each time. They can be corrected by using a different technique to take measurements.

Question 3

Precision

Answer 3

How close measurements are to each other and the mean.

Question 4

Accuracy

Answer 4

How close a measurement is to the true value.

Question 5

Repeatable

Answer 5

When the original experimenter repeats the investigation using the same method and equipment and obtains the same results.

Question 6

Reproducible

Answer 6

When somebody else repeats the investigation or the investigation is performed using different equipment or techniques and the same results are obtained.

Question 7

Resolution

Answer 7

The smallest change in a quantity being measured that gives a perceptible change in the reading.

Question 8

Readings

Answer 8

Require a single judgement.

Question 9

Measurements

Answer 9

Require two judgements.

Question 10

Uncertainty for a reading

Answer 10

+- half the smallest scale division.

Question 11

Uncertainty for a measurement

Answer 11

+- the smallest scale division.

Question 12

Base quantities and their units

Answer 12

Length (metre/m), Mass (kilogram/kg), Time (second/s), Electric current (ampere/A), Temperature (kelvin/K), Amount of substance (mole/mol), Luminous intensity (candela/cd).

Question 13

Joule in terms of base units

Answer 13

kg m^2 s^-2

Question 14

Volt in terms of base units

Answer 14

kg m^2 s^-3 A^-1

Question 15

Newton in terms of base units

Answer 15

kg m s^-2

Question 16

T, tera

Answer 16

10^12

Question 17

G, giga

Answer 17

10^9

Question 18

M, mega

Answer 18

10^6

Question 19

k, kilo

Answer 19

10^3

Question 20

c, centi

Answer 20

10^-2

Question 21

m, mili

Answer 21

10^-3

Question 22

μ, micro

Answer 22

10^-6

Question 23

n, nano

Answer 23

10^-9

Question 24

p, pico

Answer 24

10^-12

Question 25

f, femto

Answer 25

10^-15

Question 26

Number of significant figures for a calculated quantity

Answer 26

Equal to the least number of significant figures used in the calculation.

Question 27

Number of decimal places of the logarithm value

Answer 27

Equal to the number of significant figures of the value.

Question 28

Percentage uncertainty

Answer 28

The absolute uncertainty divided by the measured value multiplied by one hundred.

Question 29

When adding or subtracting data with uncertanties

Answer 29

Add the absolute uncertanties.

Question 30

When multiplying or dividing data with uncertanties

Answer 30

Add the percentage uncertanties.

Question 31

When raising data with an uncertainty to a power

Answer 31

Multiply the percentage uncertainty by that power.

Question 32

When multiplying data with an uncertainty by a constant

Answer 32

Multiply the absolute uncertainty by that constant but not the percentage uncertainty.

Question 33

Percentage uncertainty from a graph

Answer 33

|best gradient - worst gradient|/best gradient x 100% or |best y intercept - worst y intercept|/best y intercept x 100%

Question 34

Order of magnitude for the radius of a proton

Answer 34

10^-15 m

Question 35

Order of magnitude for the radius of an atom

Answer 35

10^-10 m

Question 36

Order of magnitude for the radius of the earth

Answer 36

10^7 m

Question 37

If percentage uncertainty < 1%

Answer 37

Give to 1 sig fig