Simple Question

[oupavios]

I have what should be a simple question. Can someone please explain in laymen's terms how the value of (.5 x 10^164) is greater than the value of 10^139 by more than 24 orders of magnitude? Or even how the first value exceeds the second at all?


Thanks!
Rob Campanaro

 

[stapel]

I have what should be a simple question. Can someone please explain in laymen's terms how the value of (.5 x 10^164) is greater than the value of 10^139 by more than 24 orders of magnitude? Or even how the first value exceeds the second at all?

Just use what you learned about exponents back in pre-algebra:

The first number is 0.5 * 10^164 = (5/10) * 10^164 = 5 * ((10^164)/10^1) = 5 * 10^(164-1) = 5 * 10^163. The second number is 1 * 10^139. Considering only the "orders of magnitude", you have 163 - 139 = 24.

On what mathematical or logical basis are you concluding that 5 followed by 163 zeroes, is somehow smaller than 1 followed by 139 zeroes?

 

[Deleted member 4993]

I have what should be a simple question. Can someone please explain in laymen's terms how the value of (.5 x 10^164) is greater than the value of 10^139 by more than 24 orders of magnitude? Or even how the first value exceeds the second at all?


Thanks!
Rob Campanaro

A = 0.5 x 10^164

B = 10^139

A/B = (0.5 x 10^164)/10^139 = 0.5 * 10^(164-139) = 0.5 * 10^25 >> 1 → A >> B

 

[oupavios]

Just use what you learned about exponents back in pre-algebra:

Thanks so much for the response. First, I never took any sort of advanced math in HS, and I haven't been to college. Although I did work as a programmer for a number of years. So one would think I would have a better grasp of math than I do, even without a formal education, but...

On what mathematical or logical basis are you concluding that 5 followed by 163 zeroes, is somehow smaller than 1 followed by 139 zeroes?

Well here's what I was thinking; I'm trying to determine what half of 10 ^164 is, and compare that value to 10 ^139. But when I did the calculations (.5 x 10 ^164) and 1 x 10 ^139, the calculator on my phone gave me 5.00000000E+163 and 1.00000000E+139 respectively which I didn't know how to interpret. So just looking at it, it seemed to me that half of 10 ^164 would be significantly smaller than 10 ^139 since half of 164 is 82, and 82 is significantly smaller than 139. Obviously wrong thinking.

Thanks again for your help, and in return, hopefully I gave you a good chuckle.

 

[oupavios]

Many thanks to everyone for their input.