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Scientific Notation Comparison (Negative Powers)
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00:02: Let's review how to compare numbers when they're written in scientific notation. So for each of these will compare the number on the left, to the number on the right. Remember that when you were looking in a number in scientific notation, the first thing to check is the power on the 10. If one of the numbers has a larger power than the other, then that's going to settle the issue of which number is bigger, because 3.67 times 10 to the 5th, you've gotta remember is 367 and the decimal moving five places to the right, which means you're gonna actually have three zeros. 00:44: On the other hand, 4.29 times 10 to the negative one means that you're gonna be dividing 4.29 by 10, and so you're gonna end up with 0.429. So there's really no comparison so to speak, between these numbers. The one on the left is much larger than the one on the right. But any time the power is larger, and as long as you are sure that your numbers are written in scientific notation, then that will determine the inequality. So then in this second case, we have 6.28 times 10 to the negative 10, and 9.99 times 10 to the negative 5. 01:20: So just again, apply that same principle, whichever has the larger exponent is going to be the number that is larger. In this case of course negative five is larger than negative 10. So, the number on the left is going to be less than the number on the right.
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Which number is larger?
A
B
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Answer 1

B is larger.

Reason: Compare the powers of 10 first. -5 > -10, so any number ×10^-5 is much larger than a similar-sized number ×10^-10. Concretely, 6.28×10^-10 ≈ 0.000000000628, while 9.99×10^-5 ≈ 0.0000999, so the right-hand number is larger.