Although today many use calculators and computers instead of abaci to calculate, abaci still remain in common use in some countries.Merchants, traders and clerks in some parts of Eastern Europe, Russia, China and Africa use abaci, and they are still used to teach arithmetic to children.

The woodcut shows Arithmetica instructing an algorist and an abacist (inaccurately represented as Boethius and Pythagoras).

There was keen competition between the two from the introduction of the Algebra into Europe in the 12th century until its triumph in the 16th.

Supose you have 142.57° in decimal and you need to convert to the more common degrees, minutes, and seconds (142°34'12").

What you need is called conversion from the decimal to the sexagesimal system.

The use of the word abacus dates before 1387 AD, when a Middle English work borrowed the word from Latin to describe a sandboard abacus.

The Latin word came from Greek ἄβαξ abax which means something without base, and improperly, any piece of rectangular board or plank.

0 \mbox (r_i = q_i \mbox b; q_= q_i \mbox b ; i = i 1 ) $$The converted number is composed of digits $$r_$$ (with $$r_0$$ the digit of the units). Example: $$N = 123_$$ (base 10) is converted in base $$7$$:$$ q_0 = 123 \ r_0 = 123 \mbox 7 = 4 \;\;\; q_1 = 123 \mbox 7 = 17 \ r_1 = 17 \mbox 7 = 3 \;\;\; q_1 = 17 \mbox 7 = 2 \ r_2 = 2 \mbox 7 = 2 \;\;\; q_2 = 2 \mbox 7 = 0 \ 123_ = 234_ $$To convert a number $$N_1$$ written in base $$b$$ in a number $$N_2$$ written in base $$10$$, use the fact that $$N_1$$ is made of $$n$$ digits  and apply the following algorithm:$$ N_2 = c_ ; \mbox ( i=n-2 \mbox 1 ) \mbox N_2=N_2 \times b c_i The number $$N_2$$ is written in base $$10$$.

(the exact shape of the Latin perhaps reflects the genitive form of the Greek word, ἄβακoς abakos).

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