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10=110x\times 10^{-6}
Multiply 1.1 and 100 to get 110.
10=110x\times \frac{1}{1000000}
Calculate 10 to the power of -6 and get \frac{1}{1000000}.
10=\frac{11}{100000}x
Multiply 110 and \frac{1}{1000000} to get \frac{11}{100000}.
\frac{11}{100000}x=10
Swap sides so that all variable terms are on the left hand side.
x=10\times \frac{100000}{11}
Multiply both sides by \frac{100000}{11}, the reciprocal of \frac{11}{100000}.
x=\frac{1000000}{11}
Multiply 10 and \frac{100000}{11} to get \frac{1000000}{11}.