How many times is 4 × 104 larger than 2 × 102 ?(1 point)
Responses
200
200
20
20
2,000
2,000
2
To find how many times larger 4 × 10^4 is compared to 2 × 10^2, we can divide the first expression by the second:
(4 × 10^4) / (2 × 10^2)
Simplify the division by separating the coefficients (the numbers) from the powers of 10:
(4/2) × (10^4/10^2)
4 divided by 2 gives us 2:
2 × (10^4/10^2)
Now, simplify the powers of 10 by subtracting the exponents (since we're dividing with the same base, the rule is to subtract exponents when dividing):
10^(4-2) = 10^2
Therefore, we have:
2 × 10^2
10^2 is equal to 100, so:
2 × 100 = 200
Therefore, 4 × 10^4 is 200 times larger than 2 × 10^2.