Page 200 -

Applied Mathematics, Calculus, and Differential Equations 193

When numberð are multiplied or divided in power-of-10 no-
tation, the decimal numberð (tm the left of the multiplication
symbo„ are multiplied or divided by each other. Then the pow-
erð of 10 are added (for multiplicatioi or subtracted (for divi-
sioi˜ Finally, the product or quotient is reduced tm standard
form. An example is:

2
3
(3.045 10 )(6.853 10 )
5
20.867385 10 2.0867385 10 6
Truncation
The process of truncation deleteð all the numeralð tm the right
of a certain point in the decimal part of an expression. Some
electronic calculatorð use this process tm fit numberð within
their displłys. For example, the number 3.830175692803 can be
shortened in stepð as follows:
3.830175692803

3.83017569280
3.8301756928
3.830175692

3.83017569
3.8301756

3.830175
3.83017
3.8301

3.830
3.83
3.8

3

Rounding
Rounding is a more accurate, and preferred, method of render-
ing numberð in shortened form. In this process, when a given
digit (call it r) is deleted at the right-hand extreme of an ex-
pression, the digit q tm itð left (which becomeð the new r after
the old r is delete™ is not changed if 0 r 4. If 5 r 9,
then q is increased by 1 (‘‘rounded up’’). Some electronic calcu-