RULE.--Divide as in whole numbers, annexing ciphers to the dividend, if
necessary; then point off from the right of the quotient as many places
as the decimal places in the dividend exceed those in the
divisor--prefixing ciphers if necessary.
(a) Division of a decimal by a whole number.
EXAMPLE 1: Divide 18.2754 by 4.
4)18.2754
--------
4.56885
We divide 4 into 18 (units) and have 4 (units) quotient and 3
units remainder. Since the 4 is the unit’s figure of the quotient,
we write the decimal point immediately after it. Then, the 2 units
remainder and the 2 tenths of the dividend make 22 tenths to be divided
by 4, and so on. Having reached the 4 (ten-thousandths) of the
dividend, we find 8 (ten-thousandths) quotient and 2 remainder. This
remainder is 20 hundred-thousandths, which when divided by 4 gives 5
(hundred-thousandths) and no further remainder.
EXAMPLE 2: Divide 18.2758 by 11.
11)18.2758
--------
1.66143636
Here we find the digits 3, 6 repeated indefinitely in the quotient.
Decimals of this sort will be fully considered later.
EXAMPLE 3: Divide 354.43 by 184.
184)354.43(1.92625 _Ans._
----
1704
----
483
---
1150[16]
----
460
---
920
---
Here we find the first figure of the quotient is obtained by dividing
184 into 354 units. Having now reached the decimal point in the dividend
we also put the decimal point in the answer, and go on as before.
[16] At this stage there is a remainder 115 hundredths. We bring
down 0 from the dividend, and obtain 1150 thousandths, etc.
(b) Division of a decimal.
EXAMPLE 4: Divide 10.6603 by 7.85.
Thus:
785)1066.03(1.358 _Ans._
-----
2810
----
4553
----
6280
----
Here 7.85 is 785 hundredths, and 10.6603 is 1066.03 hundredths; so that
the required quotient is obtained by dividing 1066.03 by 785.
Therefore, to divide by a decimal, move the point as many places to the
right as will make the divisor a whole number; move the point in the
dividend the same number of places to the right. Then proceed as in
Example 3.
EXAMPLE 5: Divide 176.4 by .00012.
12)17640000
---------
_Ans._ 1470000
Here, to make the divisor a whole number, we have to move the point 5
places. Therefore we also move the point 5 places to the right in the
dividend, first writing enough 0’s after the 176.4 to enable us to do
so.
To divide a decimal by 10, 100, etc.
RULE.--Remove the (.) as many places to the left as there are ciphers in
the divisor.