Solve 1+0.1(1-1/1.1)

$$1+0.1(1- \frac{ 1 }{ 1.1 } )$$

Evaluate

$$\frac{111}{110}\approx 1.009090909$$

Solution Steps

Expand \frac{1}{1.1} by multiplying both numerator and the denominator by 10.

$$1+0.1\left(1-\frac{10}{11}\right)$$

Convert 1 to fraction \frac{11}{11}.

$$1+0.1\left(\frac{11}{11}-\frac{10}{11}\right)$$

Since \frac{11}{11} and \frac{10}{11} have the same denominator, subtract them by subtracting their numerators.

$$1+0.1\times \frac{11-10}{11}$$

Subtract 10 from 11 to get 1.

$$1+0.1\times \frac{1}{11}$$

Convert decimal number 0.1 to fraction \frac{1}{10}.

$$1+\frac{1}{10}\times \frac{1}{11}$$

Multiply \frac{1}{10} times \frac{1}{11} by multiplying numerator times numerator and denominator times denominator.

$$1+\frac{1\times 1}{10\times 11}$$

Do the multiplications in the fraction \frac{1\times 1}{10\times 11}.

$$1+\frac{1}{110}$$

Convert 1 to fraction \frac{110}{110}.

$$\frac{110}{110}+\frac{1}{110}$$

Since \frac{110}{110} and \frac{1}{110} have the same denominator, add them by adding their numerators.

$$\frac{110+1}{110}$$

Add 110 and 1 to get 111.

$$\frac{111}{110}$$

Factor

$$\frac{3 \cdot 37}{2 \cdot 5 \cdot 11} = 1\frac{1}{110} = 1.009090909090909$$