Uncertainties, Prefixes and Rounding Flashcards

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1
Q

What does the prefix G stand for?

A

G stands for giga

giga = x 109

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2
Q

What does the prefix µ stand for?

A

µ stands for micro

micro = x 10-6

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3
Q

Round off this number to 3 significant figures.

3.14159

A

3.14159 rounded off to 3 significant figures is

3.14

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4
Q

Round off this number to 3 significant figures.

6.22789

A

6.22789 rounded off to 3 significant figures is

6.23

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5
Q

Round off this number to 3 significant figures.

1,526.33

A

1,526.33 rounded off to 3 significant figures is

1,530

(the ‘2’ has been rounded up to 3)

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6
Q

What does the prefix n stand for?

A

n stands for nano

nano = x 10-9

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7
Q

Round off this number to 3 significant figures.

0.0025668

A

0.0025668 rounded off to 3 significant figures is

0.00257

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8
Q

What does the prefix k stand for?

A

k stands for kilo

kilo = x 103

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9
Q

What does the prefix M stand for?

A

M stands for mega

mega = x 106

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10
Q

What does the prefix m stand for?

A

m stands for milli

milli = x 10-3

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11
Q

Equation given on formula sheet

A
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12
Q

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

A

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

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13
Q

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.

A

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

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14
Q

What type of uncertainty is revealed by repeated measurement?

A

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

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15
Q

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

A

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.

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16
Q

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

A

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

17
Q

Explain what is meant by a reading uncertainty.

A

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

18
Q

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

A

Half of the smallest division.

19
Q

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

A

One of the smallest digit.

20
Q

How do you express an uncertainty as a percentage uncertainty?

A

Percentage Unceratinty = Absolute Uncertainty/Value x 100%

21
Q

How do you calculate the uncertainty in a calculation?

A
  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.
22
Q

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.

A

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