Question

Stephen evaluated (6.34 x 10^-7)(4.5 x 10^3). His work is shown below. Which statements describe his errors? Check all that apply.

(6.34 x 10^-7)(4.5 x 10^3)
(6.34 x 4.5)(10^-7 x 10^3)
28.53 x 10^-4
-28.53 x 10^4
-2.853 x 10^3
A. He changed the sign of the coefficient. A negative exponent does not affect the sign of a coefficient in scientific notation. The sign of the exponent determines the direction the decimal is moved in.

B. He rewrote -28.53 x 10^4 incorrectly; 28.53 x 10^4 = 2.853 x 10^5. The exponent is increased to account for the extra place the decimal is moved.

C. He did not correctly evaluate the exponent. It should be evaluated as (10^-7 x 10^3) = 10^3 since exponents are evaluated using the same operation as the coefficients.

D. He got the wrong value for the coefficients; 28.53 x 10^-4 is not possible. The coefficients in scientific notation are always greater than 1, but less than 10.

F. He multiplied the coefficients; he should have added 6.34 and 4.5. The product of powers rule states that coefficients are added.

Keep in mind that there is multiple answers.

Answer 1

The correct answers to this question are the first option and the second option.

This is because a coefficient in scientific notation should always be positive, while also remain greater than 1 but less than 10.

Additionally, moving a decimal adds the value of an exponent. Hope this helps your question.

Answer 2

Answer: A. He changed the sign of the coefficient. A negative exponent does not affect the sign of a coefficient in scientific notation. The sign of the exponent determines the direction the decimal is moved in.

B. He rewrote
`-28.53*10^4` incorrectly;
`28.53* 10^4 = 2.853* 10^5`. The exponent is increased to account for the extra place the decimal is moved.

Explanation:

Given expression :
`(6.34*10^(-7))(4.5*10^3)`

`=(6.34* 4.5)(10^-7*10^3)` [Taking coefficients and exponents separate]

`=28.53*10^(-7+3)` [By law of exponent]

`=28.53*10^(-4)`

Here he changed the sign of the coefficient. A negative exponent does not affect the sign of a coefficient in scientific notation. The sign of the exponent determines the direction the decimal is moved in.

Convert in scientific form.

`28.53*10^(-4)=2.853*10*10^(-4)\\=2.853*10^(1-4)\\=2.853*10^(-3)`

In the given explanation he rewrote
`-28.53*10^4` incorrectly;
`28.53* 10^4 = 2.853* 10^5`. The exponent is increased to account for the extra place the decimal is moved.

Thus, option A and B express the errors done by Stephen.