How do I solve #0.001 = "10,000,000"/y#?

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Answer 1 · 2017-04-11T18:26:22

#y# = 10,000,000,000

Since y is at the bottom of the fraction, it can switch place with the 0.001.

#y# = #(10,000,000)/0.001#

#y# = 10,000,000,000

Answer 2 · 2017-04-11T20:07:31

Convert the numbers to powers of 10, and use the exponent laws: #10^a/10^b=10^(a-b).#

#y=10^10 = "10,000,000,000".#

Let's rewrite this question using powers of 10:

#0.001 = "10,000,000"/y#

#10^"-3"=(10^7)/y#

When we solve this for #y#, we get

#y=(10^7)/10^"-3"#

The exponent rules tell us that #10^a/10^b# is equal to #10^(a-b)#. Using this, we get

#y=(10^7)/10^"-3"=10^(7-("-3"))#
#color(white)(y=(10^7)/10^"-3")=10^(7+3)#
#color(white)(y=(10^7)/10^"-3")=10^10" "="10,000,000,000"#