Estimate Large and Small Quantities Quick Check

Question

2 of 52 of 5 Items
Question
How many times is 4 × 10^4
larger than 2 × 10^2
?(1 point)
Responses

2,000
2,000

200
200

2
2

20
20
Skip to navigation

Answer 1

To find how many times \( 4 \times 10^4 \) is larger than \( 2 \times 10^2 \), we can set up the following division:

\[ \frac{4 \times 10^4}{2 \times 10^2} \]

Now, we can simplify this step by step:

1. Divide the coefficients (4 and 2): \[ \frac{4}{2} = 2 \]

2. Now, divide the powers of 10. Recall the property of exponents: \[ \frac{10^4}{10^2} = 10^{4-2} = 10^2 \]

3. Now combine the results: \[ \frac{4 \times 10^4}{2 \times 10^2} = 2 \times 10^2 \]

4. Now, we need to interpret \( 2 \times 10^2 \): \[ 2 \times 10^2 = 2 \times 100 = 200 \]

Thus, \( 4 \times 10^4 \) is 200 times larger than \( 2 \times 10^2 \).

The correct response to your question is: 200.