Question

Shannon and Kristoph are dividing numbers written in scientific notation.

Answer 1

Answer:

Shannon's expression:

$\frac{4.2 \times 10^{9} }{1.4 \times 10^{4} }$

Kristoph's expression:

$\frac{4.2 \times 10^{2} }{1.4 \times 10^{-3} }$

(A)

Notice that both expression has the same coefficient numbers: 4.2 and 1.4. That means to have the same results, we just need to have the same powers.

Without dividing the complete expression, you can observe that both powers are the same, because each you subtract 9-4 = 5, and 2-(-3) = 5, both gives the same exponent to the power of 10.

Therefore, both expression give the same result, because they have the same numbers and the same powers.

(B)

Let's solve the division to have the result in scientific notation.

Shannon's expression:

$\frac{4.2 \times 10^{9} }{1.4 \times 10^{4} }=3 \times 10^{9-4}=3 \times 10^{5}$

Kristoph's expression:

$\frac{4.2 \times 10^{2} }{1.4 \times 10^{-3} }=3 \times 10^{2-(-3)}=3 \times 10^{5}$

(C)

The standard form refers to each number written without the power. To do so, we need to move the decimal points the number of spots as the exponent demands. Notice that the exponent is 5, that means, we need to move the decimal point 5 spots to the right.

$3 \times 10^{5}=300000$

Therefore, the standard value of the expressions is 300,000.