Page 143 - ArithBook5thEd ~ BCC

12
Example 175. Express the product (1.5 × 10 )(8 × 10 −5 )in scientific notation.
Solution. Associating the powers of 10 and the ordinary numbers, we get

12
(1.5 × 10 )(8 × 10 −5 )= 1.5 × 8 × 10 12 × 10 −5
=12 × 10 12−5
7
=12 × 10 .

This is not yet in scientific notation, since 12 is not a number between 1 and 10. But
1
12 = 1.2 × 10 ,

so the product, in scientific notation, is

1
7
12 × 10 =1.2 × 10 × 10 7
8
=1.2 × 10 .

Note how tedious this example would have been without the use of scientific notation. You would
need a large sheet of paper, and many rows of 0’s to compute
1, 500, 000, 000, 000 × 0.00008 = 120, 000, 000.

4.10.1 Exercises

Find the order of magnitude of each number.

1. 89
2. 1, 056, 503

3. 0.99

4. 0.000052

5. 8

6. 12
7. 1, 181, 000, 000, 000

Express each number in scientific notation.

8. 89

9. 1, 056, 503

10. 0.99
11. 0.000052

12. 8

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