Solve 7.84*10^-4(0.05/7.3*10^-2+0.002/0.038)=

$$7.84 \cdot 10 ^ { - 4 } ( \frac { 0.05 } { 7.3 \cdot 10 ^ { - 2 } } + \frac { 0.002 } { 0.038 } ) =$$

Evaluate

$$\frac{50127}{86687500}\approx 0.000578249$$

Solution Steps

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$7.84\times \frac{1}{10000}\left(\frac{0.05}{7.3\times 10^{-2}}+\frac{0.002}{0.038}\right)$$

Multiply 7.84 and \frac{1}{10000} to get \frac{49}{62500}.

$$\frac{49}{62500}\left(\frac{0.05}{7.3\times 10^{-2}}+\frac{0.002}{0.038}\right)$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{49}{62500}\left(\frac{0.05}{7.3\times \frac{1}{100}}+\frac{0.002}{0.038}\right)$$

Multiply 7.3 and \frac{1}{100} to get \frac{73}{1000}.

$$\frac{49}{62500}\left(\frac{0.05}{\frac{73}{1000}}+\frac{0.002}{0.038}\right)$$

Divide 0.05 by \frac{73}{1000} by multiplying 0.05 by the reciprocal of \frac{73}{1000}.

$$\frac{49}{62500}\left(0.05\times \frac{1000}{73}+\frac{0.002}{0.038}\right)$$

Multiply 0.05 and \frac{1000}{73} to get \frac{50}{73}.

$$\frac{49}{62500}\left(\frac{50}{73}+\frac{0.002}{0.038}\right)$$

Expand \frac{0.002}{0.038} by multiplying both numerator and the denominator by 1000.

$$\frac{49}{62500}\left(\frac{50}{73}+\frac{2}{38}\right)$$

Reduce the fraction \frac{2}{38} to lowest terms by extracting and canceling out 2.

$$\frac{49}{62500}\left(\frac{50}{73}+\frac{1}{19}\right)$$

Add \frac{50}{73} and \frac{1}{19} to get \frac{1023}{1387}.

$$\frac{49}{62500}\times \frac{1023}{1387}$$

Multiply \frac{49}{62500} and \frac{1023}{1387} to get \frac{50127}{86687500}.

$$\frac{50127}{86687500}$$

Factor

$$\frac{3 \cdot 11 \cdot 31 \cdot 7 ^ {2}}{19 \cdot 73 \cdot 2 ^ {2} \cdot 5 ^ {6}} = 0.0005782494592645998$$