Question

How do you multiply two scientific notation values?

Explain the steps you would take to find the product of
6.7 x 106 and 3.2 10 written in scientific notation.

Answer 1

Calculate the product of the coefficients and powers separately. Apply the product of powers rule to add the exponents. The product is not in scientific notation because the coefficient is greater than 10. Change the coefficient by moving the decimal one place to the left and increasing the exponent by one.

Explanation:

(sample response from edgenuity)

Answer 2

case 1)
`2.144*10^(12)`

case 2)
`2.144*10^(8)`

Explanation:

case 1) If we have

`6.7*10^(6)` and
`3.2*10^(5)`

step 1

Calculate the product of the coefficients and powers separately

`6.7*3.2=21.44`

`10^(6)*10^(5)` -----> Apply the product of powers rule to add the exponents

`10^(6)*10^(5)=10^(6+5)=10^(11)`

step 2

we have

`21.44*10^(11)`

The product is not in scientific notation because the coefficient is greater than 10

step 3

Change the coefficient by moving the decimal one place to the left and increasing the exponent by one

`2.144*10^(12)`

case 2) If we have

`6.7*10^(6)` and
`3.2*10^(1)`

step 1

Calculate the product of the coefficients and powers separately

`6.7*3.2=21.44`

`10^(6)*10^(1)` -----> Apply the product of powers rule to add the exponents

`10^(6)*10^(1)=10^(6+1)=10^(7)`

step 2

we have

`21.44*10^(7)`

The product is not in scientific notation because the coefficient is greater than 10

step 3

Change the coefficient by moving the decimal one place to the left and increasing the exponent by one

`2.144*10^(8)`