Evening star. [volume] (Washington, D.C.) 1854-1972, 1910-02-13
AN ODD FEATURE OF 10. 1919, ETC.

A SHORT time ago the author of this article
"A wrote for your SUNDAY MAGAZINE an arti
Gle entitled Number 81 an Oddly.
The reverse number 10 also has an odd fea
ture when used to multiply number of two
places with the same figure in each place; or,
in other words, the first nine multiples of IL,
vtg., IL, %, 49, ~, 50, &c, H. ss, and 90
Let take II times 10. The hundreds figure
of the product may be found by adding the two
Is in IL, which makes 2; while the ten and
unit figures will be the product of the units of
both numbers; thus times IS 9. AS there
is also one figure in this product, however, and
we must have two places we prefix cipher,
making 90, and the whole product will then be
200.
Likewise the product of % times 10 will be
as follows. The sum of the 2's in % gives
hundreds; and the product of the units 2
times 9 is Is; and the total product is therefore
AIS.
In the same manner the product of 33 times
10 may be found to be 627; A times 10, $50
and so on to 80 times 10, or ,SS1. The princi
pie, however, ends here and cannot be extended
to higher multip!es of II, except of course 10
times 10, where the product is simply cipher
annexed to the product of II times 10.
A slight variation of this will extend the prin-
ciple to multiplying number of three places of
the same figure (the first nine multiples of 11D
by 1879. This may be illustrated as follows:
Multiply 222 by 1899 For the hundred and
unit figures of the product, we multiply to-
gether the unit figures of both multiplicand and
multipler, 2 and 9, which gives 49, For tens
figure between hundreds and units, we take
less than units figure, viS., Z. The right hand
part of the product will therefore be IFS. For
the remaining left hand figures of the product
multiply the places of the multiplcand at
the left of units, Ufs %, by 2 which gives A
The complete product will therefore be A. IFS.
For 1888 times .999, where the figure is re-
peated four times in the multiplicand, the rule
is changed SO that the figures in the product of
units by units, Uts., 3 times 9, will occupy thou
sands and units place, the intervening places
hundreds and tens each being occupied by a
figure less than units. The right hand portion
of the product will therefore be 1867 We then
multiply all the figures of the multiplicand ex-
cept units by 2 which gives 666 for the left part
of the product.
Likewise numbers of five places containing
the same figure five times can be multiplied by
by multiplying all the figures of the multiple
cand except units by 2 for the left portion of
the product and multiplying units of multiple
cand by units of mutiplier, placing the figures
50 found in the places of the product CORE
spending to the end places of mutiplicand or
multiplier, filling the intermediate spaces
with figure less than units of product
To illustrate the rule more thoroughly, let
take the example A 444 times 10, 999 Accord
ing to the rule, we have for the left portion of
the product 4,444 times ?, or s,sss. For the
right hand figures, we have times T. or Sc
occupying then thousands and units places of
the product (the end places of both multiple
cand and multiplier being ten thousands and
units) the intermediate figure being minus /
or 5, repeated three times for thousands hun
dreds, and tens places of products. The com
plete product will therefore be SSS S:35, $50.
The rule is really very simple when thor
oughly understood, and besides being interest
ing and odd, shows how large operation in
multiplying such class of numbers may be
simpilhed. -Dvight S. Wfseman