Question

Math question

Shannon and Kristoph are dividing numbers written in scientific notation.

Shannon’s expression: 4.2 x 10^9 /1.4 x 10^4


Kristoph’s expression: 4.2 x 10^2 /1.4 x 10^-3



C) What is the value of their expressions written in standard form?

Thanks

Answer 1

- Shannon's expression in scientific notation is
`3.0 * 10^5`

- Kristoph's expression in scientific notation is
`3.0 * 10^5`

Explanation:

Given

Shannon’s expression:
`4.2 * 10^9 /1.4 * 10^4`

Kristoph’s expression:
`4.2 * 10^2 /1.4 * 10^(-3)`

Required

What is the value of their expressions written in standard form

First, we solve Shannon's expression:

`4.2 * 10^9 /1.4 * 10^4`

Writing the expression properly

`(4.2 * 10^9)/(1.4 * 10^4)`

Split into two

`(4.2)/(1.4) * (10^9)/(10^4)`

`3.0 * (10^9)/(10^4)`

From laws of indices
`(a^m)/(a^n) = a^(m-n)`

Applying the above law, we have

`3.0 * 10^(9-4)`

`3.0 * 10^5`

Hence, Shannon's expression in scientific notation is
`3.0 * 10^5`

Applying the same steps on Kristoph's expression; we have

`4.2 * 10^2 /1.4 * 10^(-3)`

Writing the expression properly

`(4.2 * 10^2)/(1.4 * 10^(-3))`

Split into two

`(4.2)/(1.4) * (10^2)/(10^(-3))`

`3.0 * (10^2)/(10^(-3))`

From laws of indices
`(a^m)/(a^n) = a^(m-n)`

Applying the above law, we have

`3.0 * 10^(2-(-3))`

`3.0 * 10^(2+3)`

`3.0 * 10^5`

Hence, Kristoph's expression in scientific notation is
`3.0 * 10^5`