Solve frac{60*10^{3}*1.2}{210*10^{8}*600*10^-6}+40*10^3*(1.2+2.4)/210*10^8*600*10^-6

$$\frac { 60 \times 10 ^ { 3 } \times 1.2 } { 210 \times 10 ^ { 8 } \times 600 \times 10 ^ { - 6 } } + \frac { 40 \times 10 ^ { 3 } \times ( 1.2 + 2.4 ) } { 210 \times 10 ^ { 8 } \times 600 \times 10 ^ { - 6 } }$$

Evaluate

$$\frac{3}{175}\approx 0.017142857$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and -6 to get 2.

$$\frac{60\times 10^{3}\times 1.2}{210\times 10^{2}\times 600}+\frac{40\times 10^{3}\left(1.2+2.4\right)}{210\times 10^{8}\times 600\times 10^{-6}}$$

To multiply powers of the same base, add their exponents. Add 8 and -6 to get 2.

$$\frac{60\times 10^{3}\times 1.2}{210\times 10^{2}\times 600}+\frac{40\times 10^{3}\left(1.2+2.4\right)}{210\times 10^{2}\times 600}$$

Cancel out 2\times 10\times 30\times 10^{2} in both numerator and denominator.

$$\frac{1.2}{7\times 30}+\frac{40\times 10^{3}\left(1.2+2.4\right)}{210\times 10^{2}\times 600}$$

Multiply 7 and 30 to get 210.

$$\frac{1.2}{210}+\frac{40\times 10^{3}\left(1.2+2.4\right)}{210\times 10^{2}\times 600}$$

Expand \frac{1.2}{210} by multiplying both numerator and the denominator by 10.

$$\frac{12}{2100}+\frac{40\times 10^{3}\left(1.2+2.4\right)}{210\times 10^{2}\times 600}$$

Reduce the fraction \frac{12}{2100} to lowest terms by extracting and canceling out 12.

$$\frac{1}{175}+\frac{40\times 10^{3}\left(1.2+2.4\right)}{210\times 10^{2}\times 600}$$

Cancel out 4\times 10\times 10\times 10^{2} in both numerator and denominator.

$$\frac{1}{175}+\frac{\frac{6+12}{5}}{15\times 21}$$

Add 6 and 12 to get 18.

$$\frac{1}{175}+\frac{\frac{18}{5}}{15\times 21}$$

Multiply 15 and 21 to get 315.

$$\frac{1}{175}+\frac{\frac{18}{5}}{315}$$

Express \frac{\frac{18}{5}}{315} as a single fraction.

$$\frac{1}{175}+\frac{18}{5\times 315}$$

Multiply 5 and 315 to get 1575.

$$\frac{1}{175}+\frac{18}{1575}$$

Reduce the fraction \frac{18}{1575} to lowest terms by extracting and canceling out 9.

$$\frac{1}{175}+\frac{2}{175}$$

Add \frac{1}{175} and \frac{2}{175} to get \frac{3}{175}.

$$\frac{3}{175}$$

Factor

$$\frac{3}{7 \cdot 5 ^ {2}} = 0.017142857142857144$$