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

wrong A And B

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.

He rewrote Negative 28.53 times 10 Superscript 4 incorrectly; 28.53 times 10 Superscript 4 Baseline = 2.853 times 10 Superscript 5. The exponent is increased to account for the extra place the decimal is moved.

Explanation:

Answer 2

We have the following expression:
(6.34 x 10 ^ -7) (4.5 x 10 ^ 3)
The solution shown is:
(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
The errors are:
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.
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.