# Are significant numbers after the decimal place

a.

Counted numbers
Counted numbers indicate an exact number of objects or people:
A class consists of 22 students.
There are 50 cars in the parking lot.

b.

Exact numbers
Exact numbers indicate an exact number:
1 kg corresponds exactly to 1000 g.
1 m corresponds exactly to 100 cm.

c.

Measured numerical values
Measured numerical values ββare obtained by comparing the object to be measured with a unit of the size to be measured:
A ruler (smallest unit, mm) is used to determine the length l of a table in cm. To determine the length as precisely as possible, several measurements are made:
l1 = 79.9 cm
l2 = 79.85 cm
l3 = 80.0 cm
l3 = 80.1 cm
The measured numbers are subject to an uncertainty, in principle you can only measure to an accuracy of 1 mm, but a value such as 79.85 cm is permissible if the experimentally determined length is exactly between the values ββ79.8 cm and 79.9 cm.

The mean value MW is given by: MW =
 79,9 + 79,85 + 80,0 + 80,1 4
= 79.9625 cm.

Since the ruler only measures to an accuracy of 1 mm, the result should not simulate a more precise measurement and should be to one decimal place:
MW = 79.96 ... cm = 80.0 cm

d.

Rounding (according to DIN 1333)

 (i) If there is a place that should be omitted (the place after the), a number smaller than 5, the number in front of the remains unchanged, all subsequent numbers are deleted. (ii) If there is a number greater than 4 at the place that should be omitted (the place after the), then the number behind the is increased by 1, all subsequent numbers are deleted.
e.

Significant digits of a numerical value

 (i) All non-zero digits of a number are. (ii) All zeros between digits are not equal to 0. (iii) All zeros to the left of a digit are not equal to 0. (iv) All zeros to the right of a digit are not equal to 0 if there is a comma.
Examples:
 7 significant digits (i) and (ii) 7 significant digits (iii), (i) and (ii) 7 significant digits (i), (ii) and (iv) 9 significant digits (iii), (i), (ii) and (iv)
f.