Measurement and uncertainties

Physics

Measurements in physics
物理学中的测量

Fundamental and derived units
基本单位和派生单位

Quantity SI unit Symbol
Mass kilogram kg
distance metre m
Time Second s
Electric current Ampere A
Amount of substance Mole mol
Temperature Kelvin K

Derived units are combinations of fundamental units. Some examples are:
派生单位由基本单位结合而成, 如:
-m/s (Unit for velocity)
-N ((kgm/{s^2})) (Unit for force)
-J ((kg{m^2}/{s^2})) (Unit for energy)

Scientific notation and metric multipliers
科学计数法和十进制

In scientific notation, values are written in the form (a \times 10^n), where a is a number within 1 and 10 and n is any integer. Some examples are:
在科学计数法中,数值被记为(a \times 10^n)的形式, a是一个1到10的数,n可以是任何整数.

The speed of light is 300000000 (m/s). In scientific notation, this is expressed as (3 \times 10^8)
光速是300000000, 用科学计数法来表示则为(3 \times 10^8).

A centimeter (cm) is (1 \over 100) of a meter (m).
In scientific notation, one cm is expressed as (1 \times 10^{-2}) m.
一厘米是(1 \over 100)米.用科学记数法1cm被表示为(1\times 10^{-2}) m

Significant figures
有效数字

For a certain value, all figures are significant, except:
对于一个确定的值,所有的数都是有效的,除了:

  • Leading zeros
    起始的零
  • Trailing zeros if this value does not have a decimal point, for example:
    没有小数点时的拖尾零,例如

12300 has 3 significant figures. The two trailing zeros are not significant.
12300有3个有效数字.这里的俩个拖尾零是没有效的.

012300 has 5 significant figures. The two leading zeros are not significant. The two trailing zeros are significant.
012300有5个有效数字.这里的俩个前导零是无效的.俩个拖尾零是有效的

When multiplying or dividing numbers, the number of significant figures of the result value should not exceed the least precise value of the calculation.
相乘或者相除时,结果的有效数字应该不超过计算的最低精确值

The number of significant figures in any answer should be consistent with the number of significant figures of the given data in the question.
答案的有效数字应该与问题所给的有效数字位数一样

Precision and Accuracy

Precision

A measurement is said to be accurate if it has little systematic errors.

Accuracy

A measurement is said to be precise if it has little random errors.
A measurement can be of great precision but be inaccurate (for example, if the instrument used had a zero offset error).

Some Line

Maximum/Minimum line: The two lines with maximum possible slope and minimum possible slope given that they both pass through all the error bars.

Line of best fit: The straight line drawn on a graph so that the average distance between the data points and the line is minimized.

The uncertainty in the intercepts of a straight line graph: The difference between the intercepts of the line of best fit and the maximum/minimum line.

The uncertainty in the gradient: The difference between the gradients of the line of best fit and the maximum/minimum line.

Random and Systematic errors
随机误差和系统误差

Random errors
随机误差

A random error, is an error which affects a reading at random.
Sources of random errors include:

  • The observer being less than perfect
  • The readability of the equipment
  • External effects on the observed item

Systematic errors
系统误差

A systematic error, is an error which occurs at each reading.
Sources of systematic errors include:

  • The observer being less than perfect in the same way every time
  • An instrument with a zero offset error
  • An instrument that is improperly calibrated