Solve (-1.231+1/1.231)0.005+(2.14+2.14/1.231^2)0.0005

$$( - 1.231 + \frac { 1 } { 1.231 } ) 0.005 + ( 2.14 + \frac { 2.14 } { 1.231 ^ { 2 } } ) 0.0005$$

Evaluate

$$-\frac{96122137}{303072200000}\approx -0.000317159$$

Solution Steps

Expand \frac{1}{1.231} by multiplying both numerator and the denominator by 1000.

$$\left(-1.231+\frac{1000}{1231}\right)\times 0.005+\left(2.14+\frac{2.14}{1.231^{2}}\right)\times 0.0005$$

Convert decimal number -1.231 to fraction -\frac{1231}{1000}.

$$\left(-\frac{1231}{1000}+\frac{1000}{1231}\right)\times 0.005+\left(2.14+\frac{2.14}{1.231^{2}}\right)\times 0.0005$$

Least common multiple of 1000 and 1231 is 1231000. Convert -\frac{1231}{1000} and \frac{1000}{1231} to fractions with denominator 1231000.

$$\left(-\frac{1515361}{1231000}+\frac{1000000}{1231000}\right)\times 0.005+\left(2.14+\frac{2.14}{1.231^{2}}\right)\times 0.0005$$

Since -\frac{1515361}{1231000} and \frac{1000000}{1231000} have the same denominator, add them by adding their numerators.

$$\frac{-1515361+1000000}{1231000}\times 0.005+\left(2.14+\frac{2.14}{1.231^{2}}\right)\times 0.0005$$

Add -1515361 and 1000000 to get -515361.

$$-\frac{515361}{1231000}\times 0.005+\left(2.14+\frac{2.14}{1.231^{2}}\right)\times 0.0005$$

Convert decimal number 0.005 to fraction \frac{5}{1000}. Reduce the fraction \frac{5}{1000} to lowest terms by extracting and canceling out 5.

$$-\frac{515361}{1231000}\times \frac{1}{200}+\left(2.14+\frac{2.14}{1.231^{2}}\right)\times 0.0005$$

Multiply -\frac{515361}{1231000} times \frac{1}{200} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-515361}{1231000\times 200}+\left(2.14+\frac{2.14}{1.231^{2}}\right)\times 0.0005$$

Do the multiplications in the fraction \frac{-515361}{1231000\times 200}.

$$\frac{-515361}{246200000}+\left(2.14+\frac{2.14}{1.231^{2}}\right)\times 0.0005$$

Fraction \frac{-515361}{246200000} can be rewritten as -\frac{515361}{246200000} by extracting the negative sign.

$$-\frac{515361}{246200000}+\left(2.14+\frac{2.14}{1.231^{2}}\right)\times 0.0005$$

Calculate 1.231 to the power of 2 and get 1.515361.

$$-\frac{515361}{246200000}+\left(2.14+\frac{2.14}{1.515361}\right)\times 0.0005$$

Expand \frac{2.14}{1.515361} by multiplying both numerator and the denominator by 1000000.

$$-\frac{515361}{246200000}+\left(2.14+\frac{2140000}{1515361}\right)\times 0.0005$$

Convert decimal number 2.14 to fraction \frac{214}{100}. Reduce the fraction \frac{214}{100} to lowest terms by extracting and canceling out 2.

$$-\frac{515361}{246200000}+\left(\frac{107}{50}+\frac{2140000}{1515361}\right)\times 0.0005$$

Least common multiple of 50 and 1515361 is 75768050. Convert \frac{107}{50} and \frac{2140000}{1515361} to fractions with denominator 75768050.

$$-\frac{515361}{246200000}+\left(\frac{162143627}{75768050}+\frac{107000000}{75768050}\right)\times 0.0005$$

Since \frac{162143627}{75768050} and \frac{107000000}{75768050} have the same denominator, add them by adding their numerators.

$$-\frac{515361}{246200000}+\frac{162143627+107000000}{75768050}\times 0.0005$$

Add 162143627 and 107000000 to get 269143627.

$$-\frac{515361}{246200000}+\frac{269143627}{75768050}\times 0.0005$$

Convert decimal number 0.0005 to fraction \frac{5}{10000}. Reduce the fraction \frac{5}{10000} to lowest terms by extracting and canceling out 5.

$$-\frac{515361}{246200000}+\frac{269143627}{75768050}\times \frac{1}{2000}$$

Multiply \frac{269143627}{75768050} times \frac{1}{2000} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{515361}{246200000}+\frac{269143627\times 1}{75768050\times 2000}$$

Do the multiplications in the fraction \frac{269143627\times 1}{75768050\times 2000}.

$$-\frac{515361}{246200000}+\frac{269143627}{151536100000}$$

Least common multiple of 246200000 and 151536100000 is 303072200000. Convert -\frac{515361}{246200000} and \frac{269143627}{151536100000} to fractions with denominator 303072200000.

$$-\frac{634409391}{303072200000}+\frac{538287254}{303072200000}$$

Since -\frac{634409391}{303072200000} and \frac{538287254}{303072200000} have the same denominator, add them by adding their numerators.

$$\frac{-634409391+538287254}{303072200000}$$

Add -634409391 and 538287254 to get -96122137.

$$-\frac{96122137}{303072200000}$$

Factor

$$-\frac{96122137}{303072200000} = -0.0003171592016687773$$