Fill in the blanks with the correct steps for solving: (3.71×105)+(4.65×107)

Question

(5 points)
Step 1:
to get the exponents the same for adding in Scientific Notation.

Step 2:
to change the coefficient on the term that the exponent was changed.

Step 3:
the coefficients.

Step 4:
exponents to simplify.

Step 5:
is the final answer in Scientific Notation.

Answer 1

To solve the expression \((3.71×10^5)+(4.65×10^7)\) in Scientific Notation, here's how you can fill in the blanks:

Step 1: Adjust the exponent of the smaller term so that both terms have the same exponent. (In this case, we will change \(10^5\) to \(10^7\).)

Step 2: Change the coefficient on the term that the exponent was changed. (For \(3.71 \times 10^5\), we change it to \(0.0371 \times 10^7\).)

Step 3: Add the coefficients. (Now you will add \(0.0371\) and \(4.65\).)

Step 4: Keep the exponents the same to simplify the final expression. (The exponent remains \(10^7\).)

Step 5: Write the final answer in Scientific Notation. (The final sum will be expressed as a coefficient multiplied by \(10^7\).)

Summarizing the full process, it looks like this:

1. Adjust the exponent of the smaller term.
2. Change the coefficient on the term that the exponent was changed.
3. Add the coefficients.
4. Keep the exponents the same to simplify.
5. Write the final answer in Scientific Notation.

Final calculation: \[ (0.0371 + 4.65) \times 10^7 = 4.6871 \times 10^7 \]

So \(4.6871 \times 10^7\) is the final answer in Scientific Notation.