Question

Stephen evaluated (6.34 times 10 Superscript negative 7 Baseline) (4.5 times 10 Superscript 3 Baseline). His work is shown below. Which two statements describe the errors Stephen made?
(6.34 times 10 Superscript negative 7 Baseline) (4.5 times 10 Superscript 3 Baseline). (6.34 times 4.5) (10 Superscript negative 7 Baseline times 10 Superscript 3 Baseline). 28.53 times 10 Superscript negative 4 Baseline. Negative 28.53 times 10 Superscript 4 Baseline. Negative 2.853 times 10 Superscript 3 Baseline.

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.

He did not correctly evaluate the exponent. It should be evaluated as (10 Superscript negative 7 Baseline times 10 Superscript 3 Baseline) = 10 Superscript negative 21 since exponents are evaluated using the same operation as the coefficients.
He got the wrong value for the coefficients; 28.53 times 10 Superscript negative 4 is not possible. The coefficients in scientific notation are always greater than 1, but less than 10.
He multiplied the coefficients; he should have added 6.34 and 4.5. The product of powers rule states that coefficients are added.

Answer 1

Steps 4 and 5 describe the errors Stephen made.

Stephen evaluated $(6.34\times 10^{-7})(4.5\times 10^3)$.  

His work is shown below.

Which two statements describe the errors Stephen made?

Step 1 - $(6.34\times 10^{-7})(4.5\times 10^3)$

Step 2 - $=(6.34\times 4.5)(10^{-7} \times 10^3)$

Step 3 - $=(28.53)(10^{-4})$

Step 4 - $20.53\times 10^4$

Error is the step as 4 sign is negative.

So correct step is $=(28.53)(10^{-4})$

Step 5 - $=(28.53)(10^{-4})$

Error is the step as there are 4 in place of 3.

So correct step is $=(28.53)(10^{-4})$

Steps 4 and 5 describe the errors Stephen made.

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