Answer:
D. There are a total of 5 decimal places in the factors. So, the product will have 5 decimal places
Step-by-step explanation:
If you were to convert these factors to integers with a multiplier of 10 to some power, they would be ...
(42×10⁻²) × (38×10⁻¹) × (1051×10⁻²)
Each of the exponents of 10 is the opposite of the number of decimal places the number had.
The product would be the product of the integers with a multiplier of 10 to the total of the powers. That total is the opposite of the total number of decimal digits in the factors.
= 1677396×10⁻⁵
Converted back to standard form, the decimal point is placed so there are 5 decimal digits:
= 16.77396
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This is basically the method we're taught to use for decimal multiplication: <em>multiply as though the numbers were integers, and place the decimal point so the total number of decimal digits in the product is equal to the total number of decimal digits in the factors</em>. (Beware products that end in 0. Those zeros are significant when you're counting decimal places.)
<em>Example</em>: 0.25 × 0.4 = 0.100 . . . . . 2+1 = 3 decimal places
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Please note that this is a description of <em>how you do multiplication of numbers with decimal fractions</em>. It is not a description of how you appropriately deal with measurement values assumed to have some associated error. The numbers here are presumed exact. A different set of rules applies to choosing an appropriate number of significant digits when measurements or estimates are involved.
