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Solution. Ignoring the decimal points, the product is 12 × 3 × 4 = 144. The numbers of decimal places
in the three decimals are, left to right, 0, 1 and 3, which add up to 4. Thus,

4
12 × 0.3 × 0.004 = 144 ÷ 10 =0.0144.

Example 166. Find the product (6.30)(−2.05).

Solution. The product is negative since the numbers have opposite signs. Temporarily ignoring the
decimal points, and the signs (i.e., working with the absolutevalues) wehave

63 0
× 20 5
31 50
1260
1291 50

Inserting a total of 4 = 2 + 2 decimal places counting from the right, and recalling that our product is
negative, we conclude that
(6.30)(−2.05) = −12.915.

4.7.1 Exercises

Find the following products.

1. 68.4 × 23

2. −804 × 6.2

3. 26.09 × 0.004

4. 4.09 × 93

5. 100 × (−9.9)

6. 14.093 × 6.39

7. 64.9 × 0.345

8. 0.0001 × 0.001

9. 1000 × 0.053

10. 6 × (−0.9) × 0.02 × (−0.001)

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