Solve 99/100-{left(297/298right)}^3

$$\frac{ 99 }{ 100 } - { \left( \frac{ 297 }{ 298 } \right) }^{ 3 }$$

Evaluate

$$\frac{22077}{661589800}\approx 0.00003337$$

Solution Steps

Calculate \frac{297}{298} to the power of 3 and get \frac{26198073}{26463592}.

$$\frac{99}{100}-\frac{26198073}{26463592}$$

Least common multiple of 100 and 26463592 is 661589800. Convert \frac{99}{100} and \frac{26198073}{26463592} to fractions with denominator 661589800.

$$\frac{654973902}{661589800}-\frac{654951825}{661589800}$$

Since \frac{654973902}{661589800} and \frac{654951825}{661589800} have the same denominator, subtract them by subtracting their numerators.

$$\frac{654973902-654951825}{661589800}$$

Subtract 654951825 from 654973902 to get 22077.

$$\frac{22077}{661589800}$$

Factor

$$\frac{3 ^ {2} \cdot 11 \cdot 223}{2 ^ {3} \cdot 5 ^ {2} \cdot 149 ^ {3}} = 3.336961966463207 \times 10^{-5}$$