Values and measurements

Содержание и основные понятия

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Alterna · physics · 0.2
Values and measurements
Physical values, SI units, division price, measurement error.
To measure is to compare with the reference. But any instrument has a limit on accuracy. Let's understand how to write the result correctly, and what is meant by "the" in L = 5.3 ± 0.05 cm.
GEF · Grade 7
PIF · Baseline
01
Physical values
The length, time, mass, temperature, speed...
Physical value
Physical value
It's a quantitative characteristic of a physical body or a phenomenon.
Examples:
length
(m),
time
(c),
Mass
(kg)
Temperature
(°C),
speed
(m/s)
volume
(m3).
SI System — International System of Units
The international system of units was adopted in 1960
SI
(Sistème International) Basic units:
Value
Unit SI
Symbol
Length
meter
m
Time
second
c
Mass
kg
kg
Temperature
Calvin
K
Current Force
Amber
A
🔗
Subtotal SI units
IV-002 · Translation between units of length, mass, time
Category
Meaning
Unit
02
Measuring instruments and division price
Any instrument has a scale. To measure, you need to know the cost of dividing.
Scale split price
The Price of Separation
- the lowest scale of the instrument. It shows which value corresponds to one compartment.
Formula:
C
= (U
max
− U
min
) / n
where
C
- The price of division,
U
max
and
U
min
- Nearly signed divisions,
n
- the number of divisions between them.
Example
There are 10 divisions between 5 cm and 6 cm in the line. The dividing price: C = (6 - 5) / 10 = 0.1 cm = 1 mm. This means that the line is measured to an accuracy of 1 mm;
📏
Cost of measuring instrument separation
IV-003 · Set the scale and calculate the price of division
Minimum scale
Maximum scale
Number of divisions:
10
03
Accuracy and error of measurements
Any measurement is inaccurate. How do you write the result correctly?
Measurement error
There are no exact measurements. The error depends on the instrument and who measures it.
Measurement error
adopted on the same date
half the price of division
instrument scales:
Δ = C / 2
The result shall be recorded as:
L = (измеренное значение) ± Δ
Example
Line 1 mm: Δ = 0.5 mm. The length of the pencil = 14.3 cm ± 0.05 cm. This means that the true length is between 14.25 and 14.35 cm.
🎰
Measurement error
IV-004 · Compare the accuracy of different lenses
Length of subject:
5.30
see
Apparatus
C
What needs to be understood
Outcome 1
Explain the physical meaning of "values and measurements" through the model, not just through the formula.
Outcome 2
Distinguish and correctly use terms: physical value, SI unit, division price.
Outcome 3
Indicate the conditions for the applicability of the law, verify units and limit cases.
T
Terms of the topic
The definition should indicate the physical meaning, not a substitute for a domestic synonym.
Physical value
The measurable property of an object or event expressed in number and unit.
SI unit
Agreement value of the physical value used to quantify homogeneous values in SI.
Diffusion price
The value of the measured value corresponding to the one smallest part of the instrument scale.
absolute error
Evaluation of the module of the possible deviation of the measurement result from the true value expressed in units of the measured value.
relative error
The ratio of absolute error to the measured value module, often expressed as a percentage.
F
Origin and conclusion of the formulas
The fundamental law cannot be "proven" by algebras: for each record, it is stated whether it is a definition, an experimental law, or a model effect.
x
=
x
изм
±
Δ
x
x=x_{\text{изм}}\pm\Delta x
x
=
x
of which:
​
±
Δ
x
definition
Recording the measurement result.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
x
min
⁡
=
x
изм
−
Δ
x
x_{\min}=x_{\text{изм}}-\Delta x
x
m
i
n
​
=
x
of which:
​
−
Δ
x
The absolute error shall be entered as an estimate of the possible deviation of the result from the measured value.
x
max
⁡
=
x
изм
+
Δ
x
x_{\max}=x_{\text{изм}}+\Delta x
x
m
a
x
​
=
x
of which:
​
+
Δ
x
The same estimate sets the upper limit of the possible value.
x
∈
[
x
изм
−
Δ
x
,
x
изм
+
Δ
x
]
x\in[x_{\text{изм}}-\Delta x,\,x_{\text{изм}}+\Delta x]
x
∈
[
x
of which:
​
−
Δ
x
,
x
of which:
​
+
Δ
x
]
A short record of ± indicates an interval, not two precisely known values.
Conditions:
Δx ≥ 0 is estimated for this method and the confidence probability; xism and Δx are recorded in the same units, the error level is agreed with the result.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
ε
=
Δ
x
∣
x
∣
⋅
100
%
\varepsilon=\frac{\Delta x}{\lvert x\rvert}\cdot100\%
ε
=
∣
x
∣
Δ
x
​
⋅
100%
definition
Relative error.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
Δ
x
∣
x
∣
\frac{\Delta x}{\lvert x\rvert}
∣
x
∣
Δ
x
​
The relative error shall be applied by comparing absolute error with the measured value module.
ε
=
Δ
x
∣
x
∣
⋅
100
%
\varepsilon=\frac{\Delta x}{\lvert x\rvert}\cdot100\%
ε
=
∣
x
∣
Δ
x
​
⋅
100%
The 100 percent increase in disproportional relationships is a percentage error.
Conditions:
x 0; Δx and x have the same units, usually using the measured value instead of the unknown true x and clearly consider the result to be an estimate.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
!
Model boundaries and typical errors
Error: Forget model condition
You can't move the formula to any situation just because the letters match. The key condition of this topic is to measure it is to compare it to the standard. But any instrument has a limit on accuracy. We can understand how to write the result correctly and what it means to write a measure in L = 5.3 ± 0.05 cm.
How to Check the Mind
The formula is only applicable after selecting the system and assumptions. Then check the unit, vector direction and result behaviour at zero or very large parameter.
Σ
Conclusion on the topic
Values and measurements
To measure is to compare with the reference. But any instrument has a limit on accuracy. Let's understand how to write the result correctly, and what is meant by "the" in L = 5.3 ± 0.05 cm.
To measure is to compare with the reference. But any instrument has a limit on accuracy. Let's understand how to write the result correctly, and what is meant by "the" in L = 5.3 ± 0.05 cm.
The formula is applicable only after the selection of the system and assumptions.
Any numerical result shall be accompanied by a unit, a sign and an explanation of its physical meaning.
The content is consistent with the FRP on Physics of the OS/OSS 2025 and the subject matter of the current lines of the PNP: I. M. Peryškin and co-authors (7–9), G. J. Mäkishev and coauthors (10–11), and with the lines "Engineers of the Future" and V. A. Kasyanov. The original texts are not reproduced, the text of the textbooks is not reproduced.