Question

Think About the Process  Find the quotient of the first factors of StartFraction 4.9 times 10 Superscript 4 Over 9.8 times 10 Superscript negative 3 EndFraction
. What do you​ notice? Find the quotient. Use pencil and paper. How does this affect the exponent of the​ quotient?
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Part 1
Divide the first factors of the given numbers. What do you​ notice?
A.
The quotient of the first factors is less than 1.
B.
The quotient of the first factors is greater than 10.
C.
The quotient of the first factors is greater than 1 but less than 10.

Answer 1

Let's find the quotient of the first factors of the expression \( \frac{4.9 \times 10^4}{9.8 \times 10^{-3}} \).

1. **Divide the first factors:**
\[
\frac{4.9}{9.8} = 0.5
\]

2. **Notice what this result tells us:**
- The quotient \( 0.5 \) is less than 1.

Thus, the correct answer to the first part, **"What do you notice?"**, is:
- **A. The quotient of the first factors is less than 1.**

Next, let's proceed to find the total quotient, incorporating the exponents.

3. **Divide the powers of ten:**
\[
\frac{10^4}{10^{-3}} = 10^{4 - (-3)} = 10^{4 + 3} = 10^7
\]

4. **Combine the results:**
The overall quotient will be:
\[
0.5 \times 10^7
\]

5. **Adjusting into scientific notation:**
In scientific notation, \( 0.5 \times 10^7 \) can be rewritten as:
\[
5.0 \times 10^6
\]

6. **Effect on the exponent:**
Since the initial quotient of the first factors was less than 1 (specifically, it was \( 0.5 \)), converting \( 0.5 \) into scientific notation increased the power of 10 (from 7 to 6), as we adjusted the decimal point to form a valid scientific notation.

In summary:
- The quotient of the first factors is less than 1 (A).
- The effect on the exponent of the quotient is that it decreases by 1 when rewriting \( 0.5 \) in standard scientific notation.