(1)
is called an absolute error. The relative error can expressed as a percentage of
,
100
a
a
(2)
Will be here is the average value of the absolute magnitude. The Grade 8
algebra textbook provides information on absolute and relative errors.
2. Scientific results and their analysis
1. In most cases the exact values of quantities are unknown, so absolute error
of approximation cannot be found. However, it is often possible to estimate
absolute error if more or less convergence is known.
1 – T a s k. The upper end of the liquid column is between 21 and 22 ° C on
a room thermometer. The approximate value of the temperature is 21.5. Estimate
the absolute error of convergence. The exact value of the temperature
△t is
unknown, but it is 21≤ t ≤22. To estimate the difference between the exact value of
the temperature and the approximate value, that is, the value of t=21.5, we subtract
21.5 from each part of this double inequality. 00.5 ≤ t ≤ 0.5, that is | t -21.5 | Let ≤
0.5. Thus, the absolute error is less than 0.5. In this case, the temperature is said to
be measured with accuracy up to 0.5 and is written as follows: t = 21.5 ± 0.5.
“Fizika va texnologik ta’lim” jurnali | Журнал “Физико-технологического
образование” | “Journal of Physics and Technology Education” 2021, № 4 (Online)
Journal of Physics and Technology Education | https//phys-tech.jspi.uz/
142
Generally, if a number x is the approximate value of x and | x -a | If ≤ h, then x is
equal to a number x and is written as follows:
x = a ± h (3)
| x-a | ≤ h inequality
a - h ≤ x≤a + h (4)
Note that double inequality is the same. For example, x = 2.43 ± 0.01 records
that x is equal to 2.43 with a precision of 0.01, that is, 2.43 - 0.01 ≤ x ≤ 2.43 + 0.01
or 2.42 ≤x ≤ It is 2.44. The numbers 2.42 and 2.44 are the approximate values of x,
respectively, with more or less the same number. In measuring the temperature
normally considered in the matter, the approximate value of the temperature is 21
or 22°C. In this case, the absolute error of each approximation does not exceed
1°C. Therefore, it is generally assumed that when measuring the temperature using
a thermometer with sections of 1°C, the measurement is made with accuracy up to
1°C.
For other measuring instruments, the measurement accuracy is usually
calculated by the smallest unit. For example, length is measured in micrometers up
to 0.01 mm, temperature is measured by medical thermometer at 0.1°C, second-
hand clock shows clock time in 1 second. Thus, the measurement error depends on
which instrument is measured. The smaller the convergence error, the more
accurate the measurement instrument. After the teacher passes the subject, they are
given a number of examples to make sure that the students understand. For
example, what does the following note mean
x = 4.9 ± 0.2; 2) x = 0.5 ± 0.15
2. The rounding of numbers is used to deal with approximate values of
various sizes in many practical matters of physics, mathematics, and technology.
For example, the rate of free fall of bodies at sea level and 45° is 9.80665 m/s
2
.
Usually this number is rounded to one in ten: 9.8. It is written as follows: g≈ 9.8
(read: g is approximately 9.8). x ≈ a means that a number x is an approximate
value.
2 – T a s k. The rectangular surface area is 35 m2 and 8 m high. Find the
width of the field. The width of the area is l meters, then l = 35: 8 = 4,375. Answer:
4,375 m. In practice, this result is usually rounded to one-tenth, that is, ≈4,3. Let's
look at the rule of rounding numbers. Require rounding 4,647 to one hundred. For
rounding with Kami we omit 180 last 7 digits, resulting in 4.64. For rounding off,
subtract the last 7 digits and multiply the previous one by one. The result is 4.65.
Absolute rounding error in the first case
|4,647-4,64|= 0,007
|
