Solve (1div(1-0.9^9)*0.1*9+0.1*1)div10=

$$(1 \div (1- { 0.9 }^{ 9 } ) \times 0.1 \times 9+0.1 \times 1) \div 10=$$

Evaluate

$$\frac{9612579511}{61257951100}\approx 0.156919703$$

Solution Steps

Calculate 0.9 to the power of 9 and get 0.387420489.

$$\frac{\frac{1}{1-0.387420489}\times 0.1\times 9+0.1\times 1}{10}$$

Subtract 0.387420489 from 1 to get 0.612579511.

$$\frac{\frac{1}{0.612579511}\times 0.1\times 9+0.1\times 1}{10}$$

Expand \frac{1}{0.612579511} by multiplying both numerator and the denominator by 1000000000.

$$\frac{\frac{1000000000}{612579511}\times 0.1\times 9+0.1\times 1}{10}$$

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

$$\frac{\frac{1000000000}{612579511}\times \frac{1}{10}\times 9+0.1\times 1}{10}$$

Multiply \frac{1000000000}{612579511} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1000000000\times 1}{612579511\times 10}\times 9+0.1\times 1}{10}$$

Do the multiplications in the fraction \frac{1000000000\times 1}{612579511\times 10}.

$$\frac{\frac{1000000000}{6125795110}\times 9+0.1\times 1}{10}$$

Reduce the fraction \frac{1000000000}{6125795110} to lowest terms by extracting and canceling out 10.

$$\frac{\frac{100000000}{612579511}\times 9+0.1\times 1}{10}$$

Express \frac{100000000}{612579511}\times 9 as a single fraction.

$$\frac{\frac{100000000\times 9}{612579511}+0.1\times 1}{10}$$

Multiply 100000000 and 9 to get 900000000.

$$\frac{\frac{900000000}{612579511}+0.1\times 1}{10}$$

Multiply 0.1 and 1 to get 0.1.

$$\frac{\frac{900000000}{612579511}+0.1}{10}$$

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

$$\frac{\frac{900000000}{612579511}+\frac{1}{10}}{10}$$

Least common multiple of 612579511 and 10 is 6125795110. Convert \frac{900000000}{612579511} and \frac{1}{10} to fractions with denominator 6125795110.

$$\frac{\frac{9000000000}{6125795110}+\frac{612579511}{6125795110}}{10}$$

Since \frac{9000000000}{6125795110} and \frac{612579511}{6125795110} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9000000000+612579511}{6125795110}}{10}$$

Add 9000000000 and 612579511 to get 9612579511.

$$\frac{\frac{9612579511}{6125795110}}{10}$$

Express \frac{\frac{9612579511}{6125795110}}{10} as a single fraction.

$$\frac{9612579511}{6125795110\times 10}$$

Multiply 6125795110 and 10 to get 61257951100.

$$\frac{9612579511}{61257951100}$$

Factor

$$\frac{29 \cdot 4127 \cdot 80317}{37 \cdot 199 \cdot 271 \cdot 307 \cdot 2 ^ {2} \cdot 5 ^ {2}} = 0.15691970329383087$$