DIVISION

Division of decimals

Unfortunately I don't have the software, if it exist,
to type a long division symbol. Therefore I will
rely on illustrating division as if it were a fraction.
This is valid since the fraction bar does mean division.
ex   4 divided by 2  will be illustrated as   4
2

Dividing by decimals is similar to dividing
by whole numbers except that we don't leave
decimals in the divisor.   ex.   3.468   is
2.4
changed to    34.68   and then we divide.  The
24

How can we arbitrarily move the decimal point?
Doesn't that change the value that the problem
represents?  Let me try to explain.

What is the answer if you multiply a number
by 1? Does the value of the number change?
The answer is that the value doesn't change.
ex  178 x 1 = 178,   4.67984 x 1 = 4.67984.
Any number multiplied by 1 gives an answer
that has the same value as the original number.
Lets go back to the problem     3.468  .   We
2.4
justify moving the decimal point by multiplying the
the problem by a form of 1.
3.468   x   10   =    34.68  .      10  =  1 and therefore
2.4          10           24             10
we have multiplied by 1 ( in a different form but still 1)
hence, we have not changed the value of the problem.
Question:  Is it really necessary to move the decimal if
it occurs in the divisor?

Changing from one unit of measure to another.

How many feet in 24 inches?

1 foot equals 12 inches. Division tells us how many

of the divisor is contained in the dividend.
is 2  This answer tells us that we have two
12 inch segments in 24. Since one 12 inch segment
equals 1 foot 2 segments equal 2 feet. Notice we divided 24 inches

by 12 inches not by 1 foot. The numbers must in the same measurement.

If you have 6 inches how many feet do you have?  We still
divide 6 inches by 12 inches to find how
many feet in 6 inches. The answer is  0.5 feet or 1/2 foot.
Lets use the metric system. Will the procedure change?  NO!
How many centimeters (cm) are in 40 millimeters (mm) ?
Well 1 cm = 10 mm.  Thus divide 40 mm by 10 mm  and
we get an answer of 4 which means there are four  10 mm segments
in 40 mm. Therefore there are 4 cm in 40 mm. Same thought process as we used in the
above example with feet and inches.  How many cm in 7 mm?   answer

Dividing by 10 or a power of ten is the reverse procedure
of multiplying by 10 or a power of 10.
Remember 10 x .43 = 4.3
100 x .43 = 43
1000 x .43 = 430 notice what happens to the
decimal point.

When you divide by 10 or power of 10 the decimal points
moves to the left and you fill in any empty
place value columns with zeros.
ex.     43.78 divided by 10 = 4.378
43.78 divided by 100 =  .4378
43.78 divided by 1000 = .04378
How many place to the left did I move the decimal point
compared to the number of zeros in the
divisor?
Try these examples  1).   78.65 divided by 10 =
2)    78.65 divided by 100 =
3)    78.65 divided by 1000 =
4)    78.65 divided by 1,000,000 =    answer