How many times is 4×10

Question

4
larger than 2×10
2
? (1 point)

20

2,000

200

2

Answer 1

To find how many times \(4 \times 10^4\) is larger than \(2 \times 10^2\), you can divide the two expressions:

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

Breaking this down step by step:

1. Start by simplifying the fraction:

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

2. Calculate \(\frac{4}{2}\):

\[ = 2 \]

3. For the powers of 10, use the property of exponents that says \(\frac{a^m}{a^n} = a^{m-n}\):

\[ = 10^{4-2} = 10^2 \]

4. Now putting it all together:

\[ = 2 \times 10^2 \]

5. Evaluating \(10^2\):

\[ 10^2 = 100 \] Thus,

\[ 2 \times 100 = 200 \]

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

The answer is 200.