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DECIMALS. I I
To Reduce a Fraction of One Denomination to a Fraction
of Another Fixed Denomination, and Approx=
imately of the Same Value.
In mechanical calculations, on drawings, and on other oc-
casions, it is very frequently necessary to reduce fractions of
other denominations to eighths, sixteenths, thirty-seconds, or
sixty-fourths. This may be done by multiplying the numerator
and the denominator of the given fraction by the number which
is to be the denominator in the new fraction, then dividing this
new numerator and denominator by the denominator of the
given fraction.
Example.
Reduce % to eighths, sixteenths, thirty-seconds, sixty-
fourths, or to hundredths.
f X t = M — o or s
/
% approximately.
o
3
or \\ approximately.
16
32
42-
I X 14 — I! I =F c / or If approximately.
f X m = in = ^~ or T%V approximately.
Thus |, instead of f , is considerably too small, namely, ^,
but f| is a great deal nearer, only T^ too large, and 0.67 is -g-^
too large.
DECIMALS.
In decimal fractions the denominator is always some power
of ten, such as tenths, hundredths, thousandths, etc.
The denominator is never written, as it is fixed by the rule
that it is 1 with as many ciphers annexed as there are figures
on the right-hand side of the decimal point.
y
2 = 0.5 = five-tenths = T%
% = 0.25 — twenty-five hundredths = T
2
o%
}i = 0.125 = one hundred and twenty-five thousandths = TV
2
o
5
o
1 y
2 = 1.5 = one and five-tenths = 1 T%
\% = 1.25 = one and twenty-five hundredths = 1 T%%, etc.
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