Think Carefully Before You Shade The Answer Sheet To Change. Do All Rough Work On This Question Paper. Now Answer The Following Question:1. Multiply $6.4 \times 10^4$ By $8.5 \times 10^4$ And Leave Your Answer In Standard Form.A.

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Think Carefully Before You Shade the Answer Sheet to Change: A Guide to Mathematics

As students, we have all been there - staring at a question paper, trying to make sense of the numbers and formulas, and hoping that we can somehow magically arrive at the correct answer. But, have you ever stopped to think about the importance of doing your rough work on the question paper? In this article, we will explore the significance of doing your rough work and provide a step-by-step guide on how to multiply two numbers in standard form.

Rough work is an essential part of the problem-solving process in mathematics. It allows you to work through the problem step-by-step, check your calculations, and ensure that you arrive at the correct answer. By doing your rough work on the question paper, you can:

  • Avoid mistakes: Rough work helps you to catch errors and mistakes before you submit your answer.
  • Save time: By working through the problem step-by-step, you can avoid wasting time on incorrect calculations.
  • Improve understanding: Rough work helps you to understand the problem and the solution, which can lead to a deeper understanding of the subject matter.

Now, let's move on to the problem at hand - multiplying two numbers in standard form. The numbers we are given are $6.4 \times 10^4$ and $8.5 \times 10^4$. To multiply these numbers, we need to follow the rules of exponentiation and multiplication.

Step 1: Multiply the Coefficients

The first step is to multiply the coefficients of the two numbers. The coefficient is the number in front of the exponent. In this case, the coefficients are 6.4 and 8.5.

6.4×8.5=54.46.4 \times 8.5 = 54.4

Step 2: Multiply the Exponents

The next step is to multiply the exponents of the two numbers. The exponent is the number that is raised to the power of 10. In this case, the exponents are 4 and 4.

104×104=104+4=10810^4 \times 10^4 = 10^{4+4} = 10^8

Step 3: Combine the Results

Now that we have multiplied the coefficients and the exponents, we can combine the results to get the final answer.

54.4×108=5.44×10954.4 \times 10^8 = 5.44 \times 10^9

In conclusion, doing your rough work on the question paper is essential to ensure that you arrive at the correct answer. By following the steps outlined above, you can multiply two numbers in standard form and arrive at the correct answer. Remember to always check your calculations and ensure that you understand the problem and the solution.

The final answer is: 5.44×109\boxed{5.44 \times 10^9}