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How do you write 8×103 in the standard notation.

Answer
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Hint: We are given a term as 8×103 and we are asked to write it in standard notation. To do so we will learn what type of notation is this and in which it is written and then we will learn about the standard notation. We will use the property that xa=x×x×x......×xa times to simplify and solve. Using this knowledge, we will be able to change 8×103 into standard notation.

Complete step-by-step solution:
We are given a term as 8×103 and if we look closely we can see that the term has one term as 8 and the other in the exponent of the base 10. So, we can understand that the form is a scientific notation form. So, here we are asked to change the scientific notation to the standard notation where the standard notation means to write the scientific term to the decimal form. To do so we have to understand how the scientific notation comes. If we have the decimal term in which non – zero terms is after 3 units from the decimal to the right, then the power of the exponent will rise to a negative of 3. For example, 0.003 it will become 3×103. And if the non – zero terms is after 3 units from the decimal to the left, then the power will rise to + 3. For example, 3000 it will become 3×103. Similarly, we just had to use this knowledge in the reverse order that is if the power of 10 is positive then the decimal will move to the right and if the power is negative then the decimal will move to the left. For example, 2.0×102 the power is positive 2. So, the decimal will move 2 units to the right. So, 2.0×102=200.0. Now, we will work on our problem. We have 8×103 so firstly we can write it as 8.0×103. Now power is positive 3. So, the decimal moves 3 units to the right. So, we get,
8.0×103=8000.0
8.0×103=8000

Note: Another way to solve is to use Algebra where we will expand the exponent and then simplify using multiplication. That is for example 2×33=2×3×3. Now, solving this, we get, 18. So in 8×103, we will expand 103 as 10×10×10. So, we get, 8×103=10×10×10. On simplifying, we get the answer as 8000. Hence 8×103 is the same as 8000.

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