Answer:
1.9532×10⁻¹¹
Explanation:
You want the product (3.8 × 10^-2)(5.14 × 10^-10) in scientific notation.
Product
The product is computed in the usual way, making use of the rules of exponents.
(3.8 × 10^-2)(5.14 × 10^-10) = (3.8×5.14) × (10^-2)(10^-10)
= 19.532 × 10^(-2-10) = 19.532 × 10^-12
Moving a factor of 10 from the coefficient to the exponent gives ...
= 1.9532×10^-11 . . . . . . final answer in scientific notation
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Additional comment
Scientific notation has 1 digit to the left of the decimal point in the coefficient.
Here, we had to divide by 10 to put the coefficient decimal point in the right place. To keep the number at the same value, we had to increase the exponent of 10 by 1 from -12 to -11.
Your calculator can display the product in scientific notation for you, as can any spreadsheet.
Sometimes it is convenient to adjust the exponents before the multiplication. Here, you can see the product of the coefficients will be greater than 10, so will ultimately need to be divided by 10. One way to get there is rewriting the problem as (0.38×10^-1)(5.14×10^-10). This will give a product coefficient between 1 and 10 with an exponent of -11.
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