01 Measurements

Question 1

z = a + b

∆z = ?

Answer 1

∆z = ∆a + ∆b

Question 2

z = ab

∆z = ?

Answer 2

∆z = z(∆a/a + ∆b/b)

Question 3

z = 3a

∆z = ?

Answer 3

∆z = 3∆a

Question 4

z = a³

∆z = ?

Answer 4

∆z = 3z(∆a/a)

Question 5

n = 5.36×10⁴ m³ ∆n = 4.3×10³ m³ (n±∆n) = ?

Answer 5

(n±∆n) = (5.4±0.4)×10⁴ m³

1. ∆n must be 1 s.f.
2. n and ∆n must be expressed to same d.p.

Question 6

State what is meant by the term accuracy.

Answer 6

Accuracy refers to how closely a measured value agrees with the ‘true’ value.

Question 7

State what is meant by a systematic error.

Answer 7

A systematic error is one that occurs according to some fixed rule or pattern such that they yield a consistent over-estimation or under-estimation of the true value of the measured quantity.

Question 8

State what is meant by a random error.

Answer 8

A random error is one that occurs without a fixed pattern such that a set of measurements done under the same conditions have an equally likely chance of being greater or less than the true value.

Question 9

State what is meant by the term precision.

Answer 9

Precision refers to how closely individual measurements agree with each other without reference to any ‘true’ value.