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16. .65 − (−6.4)
17. Subtract 5.5 from 2.4
18. Subtract −53 from 68.6
19. −8.88 − (−1.11)
1
20. Subtract 2.2 from
5
21. Find the net profit (or loss) of a business that received checks in the amounts of $453.05, $865.50
and $300.25, and paid bills in the amounts of $561.50, $449.25, $798.75 and $75.25.
22. A sunken car is salvaged from the bottom of a lake. The elevation of the lake bottom is −66.2 feet.
The car is lifted by a crane to a height 79.5 feet above lake level. Through what vertical distance
was the car lifted?
4.6 Multiplying and Dividing Decimals by Powers of 10
What happens when we multiply a whole number by 10? Ones become tens, tens become hundreds ,
hundreds become thousands ,etc. For example,in the multiplication
234 × 10 = 2340,
the 4 ones in 234 turn into the 4 tens in 2340, the 3 tens turn into 3 hundreds and so forth. (In the
product, there are no longer any ones , and that fact must be recorded with a significant 0 in the ones
place.)
Remember that a whole number is a decimal, with the decimal point understood to be immediately
to the right of the ones place. Making the decimal point explicit in our example,
234.0 × 10 = 2340.
We can describe what happens this way: when we multiply by 10, all the digits shift one place to the
left, including the insignificant 0 which was understood to be in the tenths place of the whole number
234. (In this description, we imagine the decimal point remaining fixed.) Similarly, if we multiply a
whole number by 100, all the digits shift two places to the left, including the two insignificant 0’s
which are understood to be in the tenths and hundredths places. Thus, 597 × 100 = 59 700, or, more
explicitly,
597.00 × 100 = 59 700.
n
In general, if we multiply a whole number by any positive power of 10, say, by 10 ,all the digits shift n
places to the left, including the n insignificant 0’s understood to be in the n places to the right of the
decimal point (while the decimal point remains fixed). Thus, for example,
4
281 × 10 =2 810 000.
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