Answer:
1,700
Step-by-step explanation:
5x10^-7 is 0.0000005, while 8.5x10^-4 is 0.00085
0.00085/0.0000005=1700
Thus5 x [tex]10^{-7}[/tex] is 1700 times smaller than 8.5 x [tex]10^{-4}[/tex].
Option C is the correct answer.
Given,
5 x [tex]10^{-7}[/tex] and 8.5 x [tex]10^{-4}[/tex]
We need to find how many times smaller is 5 x [tex]10^{-7}[/tex] than 8.5 x [tex]10^{-4}[/tex].
Exponents are the power of a given number.
Example: a²
a - base
2 - exponent
Compare 5 x [tex]10^{-7}[/tex] and 8.5 x [tex]10^{-4}[/tex].
5 x [tex]10^{-7}[/tex] can be written as 5 / 10000000
8.5 x [tex]10^{-4}[/tex] can be written as 8.5 / 10000
Now,
5 / 10000000 = 0.0000005
8.5 / 10000 = 85 / 100000 = 0.00085
We see that,
0.0000005 is less than 0.00085
Now,
0.0000005 x 1700 = 0.00085
5 x [tex]10^{-7}[/tex] is 1700 times smaller than 8.5 x [tex]10^{-4}[/tex].
We can also write as:
5 x [tex]10^{-7}[/tex] x 17 x 10 ²
= 5 x 17 x [tex]10^{-7}[/tex] x 10²
= 85 x [tex]10^{-7 + 2}[/tex]
= 85 x [tex]10^{-5}[/tex]
= 85/10 x 10 x [tex]10^{-5}[/tex]
= 8.5 x [tex]10^{-5 + 1}[/tex]
= 8.5 x [tex]10^{-4}[/tex]
Thus 5 x [tex]10^{-7}[/tex] is 1700 times smaller than 8.5 x [tex]10^{-4}[/tex].
Learn more about finding comparing numbers with exponents here:
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