Page 130 - ArithBook5thEd ~ BCC

If there are non-zero digits to the right of the decimal place, theyshift inexactly the same way.
Here are some examples:

38.623 × 100 = 3862.3
0.6 × 10 = 6
0.0031 × 1000 = 3.1
4
12.09 × 10 =120 900
2
100 × 10 =10000.
Note that insignificant 0’s have been omitted from the products.
It is often convenient to imagine that, when multiplying by a power of 10, the digits remain fixed
while the decimal point moves (to the right ). (Electronic calculators work this way, using a “floating”
decimal point.) This description leads to a very easy rule for multiplying a decimal by a positive power
of 10:

n
To multiply a decimal by 10 ,move the decimal point n places to the right.

If we divide adecimalby 10, hundreds becomes tens , tens become ones, ones become tenths ,
tenths become hundredths , etc. The whole discussion above can be repeated, except that,in this case
of division, digits shift to the right , or, equivalently, the decimal point moves to the left . The easy rule
is

n
To divide a decimal by 10 ,move the decimal point n places to the left.

Here are some examples:

623 ÷ 10 = 62.3
0.023 ÷ 100 = 0.00023
480 ÷ 10 = 48
3
37.5 ÷ 10 =0.0375
Example 161. Divide 3.738 ÷ (−100).

Solution. The quotient is negative because the numbers have opposite signs. Thus

3.738 ÷ (−100) = −(3.738 ÷ 100) = −0.03738.

With the convention that
1
10 −n = ,
10 n

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