Video: Number Operations in Scientific Notation

Work out the value of (5 × 10⁵) × (8.2 × 10¹¹), giving your answer in scientific notation.

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Video Transcript

Work out the value of five times 10 to the 5 times 8.2 times 10 to the power of 11, giving your answer in scientific notation.

Well, again, multiplication is commutative, so it doesn’t matter whether we’ve got the parentheses and what order we write those in. So, I’m going to do five times 8.2 times 10 to the power of five times 10 to the power of 11, in that order. Now, five times 8.2 is 41. And if I multiplied by 10 to the power of five, that’s multiplying by 10 five times, and then by 10 to the power of 11, that’s multiplying by 10 another 11 times, that’s a total of 16 times. So, it’s times 10 to the power of 16. So, that’s equal to 41 times 10 to the power of 16.

But wait a minute! That’s not our answer! This number here has to be between one and 10. 41 isn’t between one and 10. But look, I could write it as 4.1 times 10 to the power of something. Well, in fact, in this case it would be times 10 to the power of one because I need to multiply 4.1 by 10 once to turn it into 41. So, 41 is equal to 4.1 times 10 to the power of one.

And that’s the number that has to be multiplied by 10 to the power of 16. Well, we can see that we’ve got 4.1 times 10 once times 10 another 16 times, which means that’s times 10 17 times in total. And there we have it. We’ve now got our number in proper scientific notation. That first term is 4.1. That is between one and 10. And we’ve got times 10 to the power of 17.

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