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.