Exercises 159–161 will help you prepare for the material covered ...

Question

Exercises 159–161 will help you prepare for the material covered in the next section. If 6.2 is multiplied by 10^3, what does this multiplication do to the decimal point in 6.2?

Accepted Answer

Hello. Today we're going to be expanding a decimal using the scientific notation. So the problem states that when 9.4 is multiplied by 10 to the fifth, what does this operation due to the decimal point in 9.4. Alright, so what we want to do first is go ahead and write this into the scientific notation. We are told that we are multiplying 9.4 by 10 to the fifth. So the scientific notation is going to be 9.4 times 10 to the fifth. Now the important thing to know here is what exponent 10 is being raised by because this exponent tells you how many times that you are moving the decimal point and in one direction. So in this case here the exponent is positive five. Since this is positive five, that means we have an exponentially large number. So we're gonna be moving the decimal point to the right hand side. So writing 9.4 We are going to move the decimal .5 times to the right hand side. So that's going to be 1234 and five. And for every time that we're moving this decimal this number is getting larger by a multiple of 10. So The resulting value of 9.4 times 10 to the 5th is going to give us 940,000. And we can even put the decimal point right there because that's where we move the decimal from 9.4. So what does this mean? Well that means that this operation moves the decimal .5 times to the right and gives us the value of 940,000. And that means that the answer to this problem is going to be seen. So I hope this video helps you in understanding how to use the scientific notation, and I'll go ahead and see you all in the next video.