Physics Homework 7
The seven SI base units, which are comprised of:
Length - meter (m)
Time - second (s)
Amount of substance - mole (mole)
Electric current - ampere (A)
Temperature - kelvin (K)
Luminous intensity - candela (cd)
Mass - kilogram (kg)
Significant figure
Non-zero digits are always significant
Any zeros between two significant digits are significant
A final zero or trailing zeros with a decimal point are significant
Scientific notation
Scientific notation is a way of writing very large or very small numbers. A number is written in scientific
notation when a number between 1 and 10 is multiplied by a power of 10.
The proper format for scientific notation is 𝒂 × 𝟏𝟎𝒃 where a is a number or decimal number such that the
absolute value of a is greater than or equal to one and less than ten or, 1 ≤ |𝑎| < 10. b is the power of 10
required so that the scientific notation is mathematically equivalent to the original number.
Significant figure calculation
For addition and subtraction use the following rules:
1. Count the number of significant figures in the decimal portion ONLY of each number in the problem
2. Add or subtract in the normal fashion
3. Final answer may have no more significant figures to the right of the decimal than the LEAST number of
significant figures in any number in the problem.
For multiplication and division use the following rule:
1. The LEAST number of significant figures in any number of the problem determines the number of
significant figures in the answer.
2. WARNING: the rules for add/subtract are different from multiply/divide. A very common student error is
to swap the two sets of rules. Another common error is to use just one rule for both types of operations
Part A: Significant Figure Calculation
Question 1
a) 23 × 578 =
b) 34 × 698 =
c) 6612 × 971 =
d) 13 / 5723 =
e) 903123 / 517 =
f) 29103 / 5621 =
Question 2
a) 23.12 + 5.2278 =
b) 3.2113 + 6.7008 =
c) 0.143 + 9.00078 =
d) 0.23 – 1.5718 =
e) 5.8123 – 5.7128 =
f) 8.113 – 81.1298 =
Question 3
a) 54
b) 162
c) 19.155
Question 4
Decimal Form
Scientific Notation
Sig Fig
Type of Unit
(Fundamental or derived)
0.002A
200019m
0.00000187Cd
17262000000K
0.00000070020mol
Part B: Uncertainty Reading Questions
Question 1
Estimate the reading and the uncertainty in the instruments in the diagrams. (Include Units)
Example Reading
(Note: Reading value is not unique for analogue device reading, but should be very close to my reading!
too far away is definitely wrong. Uncertainty value is unique)
Picture 1
Must always show the working out for the device uncertainty
From the picture, the smallest scale division is 1mm or 0.1cm
The device is analogue device, the uncertainty for analogue device is half the smallest scale division.
Thus the uncertainty is 0.5mm or 0.05cm.
The front of the black rectangle: 2.25 ± 0.05𝑐𝑚
The end of the black rectangle: 7.24 ± 0.05𝑐𝑚
Question 2
Estimate the reading and the uncertainty in the instruments in the diagrams. (Include Units)
Question 3
Estimate the reading and the uncertainty in the instruments in the diagrams. (Include Units)
Note: This is an ammeter. An ammeter (from ampere meter) is a measuring instrument used to measure the
current in a circuit. Electric currents are measured in amperes (A)
a)
Sample Solution for Question 3 a) Picture 1
If the 2 black arrows are pointing 0 and 1, use the top row to
read the value (0,0.2,0.4,0.6,0.8,1)
If the 2 black arrows are pointing 0 and 5, use the middle
row to read the value (0,1,2,3,4,5)
If the 2 black arrows are pointing 0 and 10, use the bottom
row to read the value (0,2,4,6,8,10)
In this picture, 2 black arrows are pointing 0 and 1, use the
top row to read
From the picture, the smallest scale division is 0.2A
The device is analogue device, the uncertainty for analogue
device is half the smallest scale division.
Thus the uncertainty is 0.1A.
The temperature reading is 0.1 ± 0.1𝐴
Note: 0.05 ± 0.1𝐴 is wrong because the actual reading
value can’t be more accurate than the uncertainty of the
device.
b)
c)
Part C: Uncertainty Calculations
Question 1
Simplify the following uncertainty and write it in scientific notation
𝑎 = 121.21 ± 5.123
𝑏 = 611.21 ± 17.801
𝑐 = 1210123000 ± 67010000
𝑑 = 1871 ± 812
𝑒 = 0.00001230011 ± 0.00000000125
𝑓 = 0.000000716230011 ± 0.000000005625
Question 2
𝑎 = 110 ± 5 𝑎𝑛𝑑 𝑏 = 121 ± 3
Find 3𝑎 × 𝑏
Find 2𝑎 ÷ 7𝑏
Find 𝑎 + 𝑏
Find 𝑎 − 𝑏
Find 2𝑎 + 5𝑏
Find 𝑎 − 7𝑏
Find 𝑎 × 𝑏
Find 𝑎 ÷ 𝑏
Example full mark working out for first 2 calculation
∆3𝑎 ∆𝑏
3𝑎 × 𝑏 = 3𝑎 × 𝑏 ± 3𝑎 × 𝑏 × [
+ ]
3𝑎
𝑏
3×5
3
= 3 × 110 × 121 ± 3 × 110 × 121 × [
+
]
3 × 110 121
= 39930 ± 2805
= 39930 ± 3000 (1. 𝑠. 𝑓 𝑓𝑜𝑟 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦)
= 40000 ± 3000 = (4.0 ± 0.3) × 104
2𝑎 ÷ 7𝑏 = 2𝑎 ÷ 7𝑏 ± 2𝑎 ÷ 7𝑏 × [
∆2𝑎 ∆7𝑏
+
]
2𝑎
7𝑏
= 2 × 110 ÷ (7 × 121) ± 2 × 110 ÷ (7 × 121) × [
= 0.25974 ± 0.0182
= 0.25974 ± 0.02 (1. 𝑠. 𝑓 𝑓𝑜𝑟 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦)
= 0.26 ± 0.02
2×5
7×3
+
]
2 × 110 7 × 121