Question

When a large or small number is written in standard scientific notation, the number is expressed as the product of a number between 1 and 10, multiplied by the appropriate power of 10. For each of the following numbers, indicate what power of 10 would be appropriate when expressing the numbers in stan- dard scientific notation. a. 84,961,306 c. 0.000033812 b. 0.4870 d. 3,890,406,000,000

Answer 1

a)
`10^(7)`

c)
`10^(-5)`

b)
`10^(-1)`

d)
`10^(12)`

Explanation:

When denoting a number in scientific notation there must only be one integer and the rest of the digits must be after the decimal separator. Having this in mind you only need to count the amount of places the decimal separator has to move to restore the number to the original form. It it has to move to the right, the exponent is positive otherwise is negative:

a)
`84,961,306 = 8.4961306*10^(7)`

c)
`0.000033812 = 3.3812*10^(-5)`

b)
`0.4870 = 4.87*10^(-1)`

d)
`3,890,406,000,000 = 3.890406*10^(12)`