Question

What is the product of 5.86 × 10–7 and 3.1 × 104 1. Write the expression: (5.86 × 10–7)(3.1 × 104) 2. Rearrange the expression: (5.86 × 3.1)(10–7 ∙ 104) 3. Multiply the coefficients: (18.166)(10–7 ∙ 104) 4. Apply the product of powers: 18.166 × 10-3 5. Write in scientific notation: 1.8166 × 10n What is the value of n in the scientific notation of the product?

Answer 1

-2

Explanation:

1. Write the expression:  (5.86 × 10–7)(3.1 × 104)

2. Rearrange the expression:  (5.86 × 3.1)(10–7 ∙ 104)

3. Multiply the coefficients: (18.166)(10–7 ∙ 104)

4. Apply the product of powers: 18.166 × 10-3

5. Write in scientific notation:  1.8166 × 10n

do all this get negitive two

Answer 2

The value of the exponent of the base 10 for this product is -2.

Explanation:

`5.86\,\,10^(-7)\,\,*\,\,3.1\,\,10^4=18.166\,\,10^(-7+4)=18.166\,\,10^(-3)`

Now, in order to represent this number in scientific notation, we need to reduce the coefficient 18.166 to a coefficient larger or equal to 1 and smaller strictly than 10, by using division or multiplications by powers of 10. In order to reduce it to 1.8166, we need to divide the original 18.166 by ten so we do the following in order not to change the given number (multiply and divide by ten at the same time):

`(18.166\,\,10)/(10) \,10^(-3)=1.8166\,*\,10\,*\,10^(-3)=1.8166\,\,10^(-2)`