Uncertainties, Prefixes and Rounding

Question 1

What does the prefix G stand for?

Answer 1

G stands for giga

giga = x 10⁹

Question 2

What does the prefix µ stand for?

Answer 2

µ stands for micro

micro = x 10^-6

Question 3

Round off this number to 3 significant figures.

3.14159

Answer 3

3.14159 rounded off to 3 significant figures is

3.14

Question 4

Round off this number to 3 significant figures.

6.22789

Answer 4

6.22789 rounded off to 3 significant figures is

6.23

Question 5

Round off this number to 3 significant figures.

1,526.33

Answer 5

1,526.33 rounded off to 3 significant figures is

1,530

(the ‘2’ has been rounded up to 3)

Question 6

What does the prefix n stand for?

Answer 6

n stands for nano

nano = x 10^-9

Question 7

Round off this number to 3 significant figures.

0.0025668

Answer 7

0.0025668 rounded off to 3 significant figures is

0.00257

Question 8

What does the prefix k stand for?

Answer 8

k stands for kilo

kilo = x 10³

Question 9

What does the prefix M stand for?

Answer 9

M stands for mega

mega = x 10⁶

Question 10

What does the prefix m stand for?

Answer 10

m stands for milli

milli = x 10^-3

Question 11

Equation given on formula sheet

Question 12

Explain what is meant by a random uncertainty, giving an example.

Answer 12

Random uncertainties are caused by random variations in experimental conditions e.g. random variations in background light levels due to changes in cloud cover.

Question 13

Example

A length of card was measured by six people. The following
measurements were obtained: 21cm, 24cm, 22cm, 26cm, 25cm, 22cm.
Calculate the mean value with its random uncertainty.

Answer 13

Mean length = (21 + 24 + 22 + 26 + 25 + 22)/6
= 23.33 cm

Random Uncertainty = (highest value - lowest value)/number of measurements
= (26-21)/6
= 0.83 cm
= 0.8 cm to 1 sig fig and round mean to same decimal places

length = 23.3 ± 0.8 cm

Question 14

What type of uncertainty is revealed by repeated measurement?

Answer 14

Random uncertainties would be revealed by variation in the measured values.

Question 15

Explain what is meant by a systematic uncertainty, giving an example.

Answer 15

A systematic uncertainty is caused by incorrect use of equipment or faulty equipment that results in all readings being too high or low by a fixed amount e.g. not zeroing scales before using them.

Question 16

How would you identify a systematic uncertainity was present in results?

Answer 16

A best fit line that was expected to go through the origin, is not close to the origin.

Question 17

Explain what is meant by a reading uncertainty.

Answer 17

A reading uncertainty is a measure of how well an instrument scale
can be read.

Question 18

What is the rule for reading uncertainty for an analogue instrument?

Answer 18

Half of the smallest division.

Question 19

What is the rule for reading uncertainty for a digital instrument?

Answer 19

One of the smallest digit.

Question 20

How do you express an uncertainty as a percentage uncertainty?

Answer 20

Percentage Unceratinty = Absolute Uncertainty/Value x 100%

Question 21

How do you calculate the uncertainty in a calculation?

Answer 21

1. Express the uncertainty for each value in the formula as a percentage uncertainty
2. Identify the largest percentage uncertainty and use this for the calculated value.

Question 22

Example

To find the instantaneous speed of a trolley the trolley with card was
passed through a light-gate connected to a timer. The following sets of readings were taken:
mean time = 0.028 ± 0.001 s
length of card = 120 ± 1mm

Calculate the instantaneous speed and the absolute uncertainty in this value.

Answer 22

v = s/t = 0.12/0.028 = 4.29 ms^-1

percentage uncertainty in time = 0.001/0.028 x 100 = 3.6%
percentage uncertainty in distance = 1/120 x 100 = 0.8%

The larger of these is 3.6% so this can be taken as a reasonable estimate of the uncertainty in the speed.
so, v = 4.29 ms^-1 ± 3.6%
3.6/100 x 4.29 = 0.15
= 4.29 ± 0.15 ms^-1