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182×(2.49×10−15)182×(2.49×10 −15 )  Give your final answer in scientific notation rounded to two decimal places.

Question

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Solution

1. Break Down the Problem

We need to calculate the product of two numbers: 182 182 and 2.49×1015 2.49 \times 10^{-15} .

2. Relevant Concepts

The formula for multiplying a regular number by a number in scientific notation is: a×(b×10n)=(a×b)×10n a \times (b \times 10^n) = (a \times b) \times 10^n

Where:

  • a=182 a = 182
  • b=2.49 b = 2.49
  • n=15 n = -15

3. Analysis and Detail

We will multiply 182 182 by 2.49 2.49 : 182×2.49=453.18 182 \times 2.49 = 453.18 Now, we need to express this result in scientific notation.

4. Verify and Summarize

To convert 453.18 453.18 into scientific notation: 453.18=4.5318×102 453.18 = 4.5318 \times 10^2 Now we combine this with 1015 10^{-15} : 4.5318×102×1015=4.5318×1013 4.5318 \times 10^2 \times 10^{-15} = 4.5318 \times 10^{-13}

Final Answer

Rounding 4.5318 4.5318 to two decimal places gives us: 4.53×1013 \boxed{4.53 \times 10^{-13}}

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