# Why is 12 such a significant number?

**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 ββare 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:

l_{1} = 79.9 cm

l_{2} = 79.85 cm

l_{3} = 80.0 cm

l_{3} = 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 ββ79.8 cm and 79.9 cm.

The mean value MW is given by: MW = |
| = 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. |

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.**

Addition and subtraction

The result of these operations is rounded off with the same number of digits in the number.

Counted numbers and exact numbers are not taken into account, because they have no influence on the number of decimal places.

12,25 + 14,65 + 3, + 7,203 + 0,3675 = 37,5705 = 37,6

**G.**

Multiplication and division

The result of these operations is rounded off with the same number of digits in the number.

Counted numbers and exact numbers are not taken into account because they have no influence on the number of significant digits.

12,25 · 0, = 9,1875 = 9,2

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