Solve 78/0.13<7.8/13<0.0078/0.0000013

$$\frac{ 78 }{ 0.13 } < \frac{ 7.8 }{ 13 } < \frac{ 0.0078 }{ 0.0000013 }$$

Verify

Solution Steps

Expand \frac{78}{0.13} by multiplying both numerator and the denominator by 100.

$$\frac{7800}{13}<\frac{7.8}{13}\text{ and }\frac{7.8}{13}<\frac{0.0078}{0.0000013}$$

Divide 7800 by 13 to get 600.

$$600<\frac{7.8}{13}\text{ and }\frac{7.8}{13}<\frac{0.0078}{0.0000013}$$

Expand \frac{7.8}{13} by multiplying both numerator and the denominator by 10.

$$600<\frac{78}{130}\text{ and }\frac{7.8}{13}<\frac{0.0078}{0.0000013}$$

Reduce the fraction \frac{78}{130} to lowest terms by extracting and canceling out 26.

$$600<\frac{3}{5}\text{ and }\frac{7.8}{13}<\frac{0.0078}{0.0000013}$$

Convert 600 to fraction \frac{3000}{5}.

$$\frac{3000}{5}<\frac{3}{5}\text{ and }\frac{7.8}{13}<\frac{0.0078}{0.0000013}$$

Compare \frac{3000}{5} and \frac{3}{5}.

$$\text{false}\text{ and }\frac{7.8}{13}<\frac{0.0078}{0.0000013}$$

Expand \frac{7.8}{13} by multiplying both numerator and the denominator by 10.

$$\text{false}\text{ and }\frac{78}{130}<\frac{0.0078}{0.0000013}$$

Reduce the fraction \frac{78}{130} to lowest terms by extracting and canceling out 26.

$$\text{false}\text{ and }\frac{3}{5}<\frac{0.0078}{0.0000013}$$

Expand \frac{0.0078}{0.0000013} by multiplying both numerator and the denominator by 10000000.

$$\text{false}\text{ and }\frac{3}{5}<\frac{78000}{13}$$

Divide 78000 by 13 to get 6000.

$$\text{false}\text{ and }\frac{3}{5}<6000$$

Convert 6000 to fraction \frac{30000}{5}.

$$\text{false}\text{ and }\frac{3}{5}<\frac{30000}{5}$$

Compare \frac{3}{5} and \frac{30000}{5}.

$$\text{false}\text{ and }\text{true}$$

The conjunction of \text{false} and \text{true} is \text{false}.

$$\text{false}$$