Solve 46.06*10^3/2.303*0.083[1/400-1/700]

$$\frac { 46.06 \times 10 ^ { 3 } } { 2.303 \times 0.083 } [ \frac { 1 } { 400 } - \frac { 1 } { 700 } ]$$

Evaluate

$$\frac{150000}{581}\approx 258.17555938$$

Solution Steps

Calculate 10 to the power of 3 and get 1000.

$$\frac{46.06\times 1000}{2.303\times 0.083}\left(\frac{1}{400}-\frac{1}{700}\right)$$

Multiply 46.06 and 1000 to get 46060.

$$\frac{46060}{2.303\times 0.083}\left(\frac{1}{400}-\frac{1}{700}\right)$$

Multiply 2.303 and 0.083 to get 0.191149.

$$\frac{46060}{0.191149}\left(\frac{1}{400}-\frac{1}{700}\right)$$

Expand \frac{46060}{0.191149} by multiplying both numerator and the denominator by 1000000.

$$\frac{46060000000}{191149}\left(\frac{1}{400}-\frac{1}{700}\right)$$

Reduce the fraction \frac{46060000000}{191149} to lowest terms by extracting and canceling out 2303.

$$\frac{20000000}{83}\left(\frac{1}{400}-\frac{1}{700}\right)$$

Least common multiple of 400 and 700 is 2800. Convert \frac{1}{400} and \frac{1}{700} to fractions with denominator 2800.

$$\frac{20000000}{83}\left(\frac{7}{2800}-\frac{4}{2800}\right)$$

Since \frac{7}{2800} and \frac{4}{2800} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20000000}{83}\times \frac{7-4}{2800}$$

Subtract 4 from 7 to get 3.

$$\frac{20000000}{83}\times \frac{3}{2800}$$

Multiply \frac{20000000}{83} times \frac{3}{2800} by multiplying numerator times numerator and denominator times denominator.

$$\frac{20000000\times 3}{83\times 2800}$$

Do the multiplications in the fraction \frac{20000000\times 3}{83\times 2800}.

$$\frac{60000000}{232400}$$

Reduce the fraction \frac{60000000}{232400} to lowest terms by extracting and canceling out 400.

$$\frac{150000}{581}$$

Factor

$$\frac{3 \cdot 2 ^ {4} \cdot 5 ^ {5}}{7 \cdot 83} = 258\frac{102}{581} = 258.1755593803787$$