CIE AS & A Level Physics 9702: Topic 1: Physical quantities and units- Unit : 1.3 Errors and uncertainties Study Notes

Significant number

  •  Magnitudes of physical quantities are often quoted in terms of significant number.
  •  Can you tell how many sig. fig. in these numbers?
  •  103, 100.0, 0.030, 0.4004, 200
  •  If you multiply 2.3 and 1.45, how many sf should you quote?
  •  3.19, 3.335, 3.48
  •  3.312, 3.335, $3 \cdot 358$

The rules for identifying significant figures

  • The rules for identifying significant figures when writing or interpreting numbers are as follows:-
  • All non-zero digits are considered significant. For example, 91 has two significant figures ( 9 and 1 ), while 123.45 has five significant figures $(1,2,3,4$ and 5$)$.
  • Zeros appearing anywhere between two non-zero digits are significant. Example: 101.1203 has seven significant figures: $1,0,1,1,2,0$ and 3.
  • Leading zeros are not significant. For example, 0.00052 has two significant figures: 5 and 2.

The rules for identifying significant figures (cont)

  • Trailing zeros in a number containing a decimal point are significant. For example, 12.2300 has six significant figures: $1,2,2,3,0$ and 0 . The number 0.000122300 still has only six significant figures (the zeros before the 1 are not significant). In addition, 120.00 has five significant figures since it has three trailing zeros.
  •  Often you will be asked to estimate some magnitudes of physical quantities around you.
  • E.g. estimate the height of the ceiling, volume of an apple, mass of an apple, diameter of a strand of hair,

Estimates of physical quantities

When making an estimate, it is only reasonable to give the figure to 1 or at most 2 significant figures since an estimate is not very precise.

$\begin{array}{cc}\text { Physical Quantity } & \text { Reasonable Estimate } \\ \text { Mass of } 3 \text { cans }(330 \mathrm{ml}) \text { of } & 1 \mathrm{~kg} \\ \text { Pepsi } & 1000 \mathrm{~kg} \\ \text { Mass of a medium-sized car } & 100 \mathrm{~m} \\ \text { Length of a football field } & 0.2 \mathrm{~s}\end{array}$

  • Occasionally, students are asked to estimate the area under a graph. The usual method of counting squares within the enclosed area is used.

Convention for labelling tables and graphs

The symbol / unit is indicated at the italics as indicated in the data column left.
Then fill in the data with pure numbers.
Then plot the graph after labelling x axis and y axis

[Illustration with sample graph on left]


  • For very large or very small numbers, we can use standard prefixes with the base units.
  •  The main prefixes that you need to know are shown in the table. (next slide)


  • Prefixes simplify the writing of very large or very small quantities


  • Alternative writing method
  •  Using standard form
  •  $N \times 10^n$ where $1 \leq N<10$ and $n$ is an integer

This galaxy is about $2.5 \times 10^6$ light years from the Earth.               The diameter of this atom is about $1 \times 10^{-10} \mathrm{~m}$.

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