Final answer:
To find out how many times larger 4x10^4 is than 2x10^2, divide the first number by the second resulting in a factor of 200. This shows that 4x10^4 is 200 times larger than 2x10^2.
Step-by-step explanation:
When comparing the magnitudes of two numbers written in scientific notation, like 4x10^4 and 2x10^2, you can divide the first number by the second to find out how many times larger the first number is than the second. Let's calculate this step by step:
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- Step 1: Write down the numbers 4x10^4 and 2x10^2.
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- Step 2: Divide 4x10^4 by 2x10^2 to find the ratio between them. The coefficient 4 divided by 2 gives us 2.
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- Step 3: When dividing powers of ten, you subtract the exponents. In this case, 10^4 divided by 10^2 gives us 10^(4-2), which simplifies to 10^2.
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- Step 4: Combine the coefficient and the power of ten: 2 x 10^2.
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- Step 5: Convert 10^2 into its numerical value, which is 100. Then, multiply 2 by 100 to obtain the final answer of 200.
Therefore, 4x10^4 is 200 times larger than 2x10^2.