Instruction
1
The number system is an integral part of mathematical theory that are responsible for symbolic record numbers. Each system has its own arithmetic, the set of actions: addition, multiplication, division, and multiplication.
2
The basis of the quinary system is the figure 5. Accordingly, this number represents one category, for example, 132 in the quinary system is a 2•5^0 + 3•51 + 1•52 = 2 + 15 + 25 = 42 in decimal.
3
To put the number in the quinary system from any other positional number system, use the method of successive division. The required number divide by 5, recording the intermediate residues in the reverse order, i.e. from right to left.
4
Start with the decimal system. Move number 69:69/5 = 13 → 4 in the remainder;13/5 = 2 → 3;2/5 = 0 → 2.
5
So, it turned out the number 234. Check the result: 234 = 4•1 + 3•5 + 2•25 = 69.
6
To translate the number from any other system in two ways: either the same logical division, or using an intermediate system, the most convenient option which will be a decimal. Despite the presence of an additional stage, the second method is faster and more accurate because it does not involve action unusual arithmetic. For example, give the octal number 354 for quinary mind.
7
Use the first method:354/5 = 57 → 1 in the remainder;57/5 = 11 → 2;11/5 = 1 → 4;1/5 = 0 → 1.
8
Uncomfortable, isn't it? All the time you need to remember that the dividend number has a bit width equal to 8, not 10, although trained on decimal operations for eyes perceive it that way. Now apply the second method:Go to decimal form: 354 = 4•1 + 5•8 +3•64= 236.
9
Do the usual translation:236/5 = 47 → 1;47/5 = 9 → 2;9/5 = 1 → 4;1/5 = 0 → 1.
10
Record the result: 354_8 = 1421_5. Check: 1421=1•1+2*5+4•25+1•125=236.