Solve 1.491+1/49+1/64+1/81+1/100

$$1.491 + \frac { 1 } { 49 } + \frac { 1 } { 64 } + \frac { 1 } { 81 } + \frac { 1 } { 100 }$$

Evaluate

$$\frac{49195877}{31752000}\approx 1.549378842$$

Solution Steps

Convert decimal number 1.491 to fraction \frac{1491}{1000}.

$$\frac{1491}{1000}+\frac{1}{49}+\frac{1}{64}+\frac{1}{81}+\frac{1}{100}$$

Least common multiple of 1000 and 49 is 49000. Convert \frac{1491}{1000} and \frac{1}{49} to fractions with denominator 49000.

$$\frac{73059}{49000}+\frac{1000}{49000}+\frac{1}{64}+\frac{1}{81}+\frac{1}{100}$$

Since \frac{73059}{49000} and \frac{1000}{49000} have the same denominator, add them by adding their numerators.

$$\frac{73059+1000}{49000}+\frac{1}{64}+\frac{1}{81}+\frac{1}{100}$$

Add 73059 and 1000 to get 74059.

$$\frac{74059}{49000}+\frac{1}{64}+\frac{1}{81}+\frac{1}{100}$$

Least common multiple of 49000 and 64 is 392000. Convert \frac{74059}{49000} and \frac{1}{64} to fractions with denominator 392000.

$$\frac{592472}{392000}+\frac{6125}{392000}+\frac{1}{81}+\frac{1}{100}$$

Since \frac{592472}{392000} and \frac{6125}{392000} have the same denominator, add them by adding their numerators.

$$\frac{592472+6125}{392000}+\frac{1}{81}+\frac{1}{100}$$

Add 592472 and 6125 to get 598597.

$$\frac{598597}{392000}+\frac{1}{81}+\frac{1}{100}$$

Least common multiple of 392000 and 81 is 31752000. Convert \frac{598597}{392000} and \frac{1}{81} to fractions with denominator 31752000.

$$\frac{48486357}{31752000}+\frac{392000}{31752000}+\frac{1}{100}$$

Since \frac{48486357}{31752000} and \frac{392000}{31752000} have the same denominator, add them by adding their numerators.

$$\frac{48486357+392000}{31752000}+\frac{1}{100}$$

Add 48486357 and 392000 to get 48878357.

$$\frac{48878357}{31752000}+\frac{1}{100}$$

Least common multiple of 31752000 and 100 is 31752000. Convert \frac{48878357}{31752000} and \frac{1}{100} to fractions with denominator 31752000.

$$\frac{48878357}{31752000}+\frac{317520}{31752000}$$

Since \frac{48878357}{31752000} and \frac{317520}{31752000} have the same denominator, add them by adding their numerators.

$$\frac{48878357+317520}{31752000}$$

Add 48878357 and 317520 to get 49195877.

$$\frac{49195877}{31752000}$$

Factor

$$\frac{2137 \cdot 23021}{2 ^ {6} \cdot 3 ^ {4} \cdot 5 ^ {3} \cdot 7 ^ {2}} = 1\frac{17443877}{31752000} = 1.5493788422776518$$