Final answer:
Scientific notation is used to express large or small numbers as a product of a number between 1 and 10 and a power of 10. The correct scientific notation for the given examples includes both positive and negative powers of ten based on whether the number is greater or less than one.
Step-by-step explanation:
Expressing numbers in scientific notation helps to simplify large or small numbers by representing them as a product of a number between 1 and 10 and a power of 10. Here are the numbers expressed in scientific notation:
a. -890,000 = -8.9 x 105
b. 602,000,000,000 = 6.02 x 1011
c. 0.0000004099 = 4.099 x 10-7
d. 0.000000000000011 = 1.1 x 10-14
a. 0.00656 = 6.56 x 10-3
b. 65,600 = 6.56 x 104
Correcting numbers that are not in proper scientific notation involves ensuring that the number before the multiplication sign is between 1 and 10:
a. 8,099 x 107 should be rewritten as 8.099 x 109
b. 34.5 x 100 is already in scientific notation because 34.5 is between 1 and 10.
c. 0.000332 x 104 should be rewritten as 3.32 x 10-1