Solve (3.8*1.75div10-1.02)div100+0.4*2.6^2+0.1^3

$$(3.8 \times 1.75 \div 10-1.02) \div 100+0.4 \times { 2.6 }^{ 2 } + { 0.1 }^{ 3 }$$

Evaluate

$$2.70145$$

Solution Steps

Multiply 3.8 and 1.75 to get 6.65.

$$\frac{\frac{6.65}{10}-1.02}{100}+0.4\times 2.6^{2}+0.1^{3}$$

Expand \frac{6.65}{10} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{665}{1000}-1.02}{100}+0.4\times 2.6^{2}+0.1^{3}$$

Reduce the fraction \frac{665}{1000} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{133}{200}-1.02}{100}+0.4\times 2.6^{2}+0.1^{3}$$

Convert decimal number 1.02 to fraction \frac{102}{100}. Reduce the fraction \frac{102}{100} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{133}{200}-\frac{51}{50}}{100}+0.4\times 2.6^{2}+0.1^{3}$$

Least common multiple of 200 and 50 is 200. Convert \frac{133}{200} and \frac{51}{50} to fractions with denominator 200.

$$\frac{\frac{133}{200}-\frac{204}{200}}{100}+0.4\times 2.6^{2}+0.1^{3}$$

Since \frac{133}{200} and \frac{204}{200} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{133-204}{200}}{100}+0.4\times 2.6^{2}+0.1^{3}$$

Subtract 204 from 133 to get -71.

$$\frac{-\frac{71}{200}}{100}+0.4\times 2.6^{2}+0.1^{3}$$

Express \frac{-\frac{71}{200}}{100} as a single fraction.

$$\frac{-71}{200\times 100}+0.4\times 2.6^{2}+0.1^{3}$$

Multiply 200 and 100 to get 20000.

$$\frac{-71}{20000}+0.4\times 2.6^{2}+0.1^{3}$$

Fraction \frac{-71}{20000} can be rewritten as -\frac{71}{20000} by extracting the negative sign.

$$-\frac{71}{20000}+0.4\times 2.6^{2}+0.1^{3}$$

Calculate 2.6 to the power of 2 and get 6.76.

$$-\frac{71}{20000}+0.4\times 6.76+0.1^{3}$$

Multiply 0.4 and 6.76 to get 2.704.

$$-\frac{71}{20000}+2.704+0.1^{3}$$

Convert decimal number 2.704 to fraction \frac{2704}{1000}. Reduce the fraction \frac{2704}{1000} to lowest terms by extracting and canceling out 8.

$$-\frac{71}{20000}+\frac{338}{125}+0.1^{3}$$

Least common multiple of 20000 and 125 is 20000. Convert -\frac{71}{20000} and \frac{338}{125} to fractions with denominator 20000.

$$-\frac{71}{20000}+\frac{54080}{20000}+0.1^{3}$$

Since -\frac{71}{20000} and \frac{54080}{20000} have the same denominator, add them by adding their numerators.

$$\frac{-71+54080}{20000}+0.1^{3}$$

Add -71 and 54080 to get 54009.

$$\frac{54009}{20000}+0.1^{3}$$

Calculate 0.1 to the power of 3 and get 0.001.

$$\frac{54009}{20000}+0.001$$

Convert decimal number 0.001 to fraction \frac{1}{1000}.

$$\frac{54009}{20000}+\frac{1}{1000}$$

Least common multiple of 20000 and 1000 is 20000. Convert \frac{54009}{20000} and \frac{1}{1000} to fractions with denominator 20000.

$$\frac{54009}{20000}+\frac{20}{20000}$$

Since \frac{54009}{20000} and \frac{20}{20000} have the same denominator, add them by adding their numerators.

$$\frac{54009+20}{20000}$$

Add 54009 and 20 to get 54029.

$$\frac{54029}{20000}$$

Factor

$$\frac{97 \cdot 557}{2 ^ {5} \cdot 5 ^ {4}} = 2\frac{14029}{20000} = 2.70145$$