Solve (5.21div1000):554div[(5-21div1000)+148]

$$( 5.21 \div 1000 ) : 554 \div [ ( 5 - 21 \div 1000 ) + 148 ]$$

Evaluate

$$\frac{521}{8475036600}\approx 0.000000061$$

Solution Steps

Express \frac{\frac{5.21}{1000}}{554} as a single fraction.

$$\frac{\frac{5.21}{1000\times 554}}{5-\frac{21}{1000}+148}$$

Multiply 1000 and 554 to get 554000.

$$\frac{\frac{5.21}{554000}}{5-\frac{21}{1000}+148}$$

Expand \frac{5.21}{554000} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{521}{55400000}}{5-\frac{21}{1000}+148}$$

Convert 5 to fraction \frac{5000}{1000}.

$$\frac{\frac{521}{55400000}}{\frac{5000}{1000}-\frac{21}{1000}+148}$$

Since \frac{5000}{1000} and \frac{21}{1000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{521}{55400000}}{\frac{5000-21}{1000}+148}$$

Subtract 21 from 5000 to get 4979.

$$\frac{\frac{521}{55400000}}{\frac{4979}{1000}+148}$$

Convert 148 to fraction \frac{148000}{1000}.

$$\frac{\frac{521}{55400000}}{\frac{4979}{1000}+\frac{148000}{1000}}$$

Since \frac{4979}{1000} and \frac{148000}{1000} have the same denominator, add them by adding their numerators.

$$\frac{\frac{521}{55400000}}{\frac{4979+148000}{1000}}$$

Add 4979 and 148000 to get 152979.

$$\frac{\frac{521}{55400000}}{\frac{152979}{1000}}$$

Divide \frac{521}{55400000} by \frac{152979}{1000} by multiplying \frac{521}{55400000} by the reciprocal of \frac{152979}{1000}.

$$\frac{521}{55400000}\times \frac{1000}{152979}$$

Multiply \frac{521}{55400000} times \frac{1000}{152979} by multiplying numerator times numerator and denominator times denominator.

$$\frac{521\times 1000}{55400000\times 152979}$$

Do the multiplications in the fraction \frac{521\times 1000}{55400000\times 152979}.

$$\frac{521000}{8475036600000}$$

Reduce the fraction \frac{521000}{8475036600000} to lowest terms by extracting and canceling out 1000.

$$\frac{521}{8475036600}$$

Factor

$$\frac{521}{3 \cdot 277 \cdot 50993 \cdot 2 ^ {3} \cdot 5 ^ {2}} = 6.147466077019656 \times 10^{-8}$$