Solve 0.0078/0.0000013<78/0.13<0.0078/0.0000013

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

Verify

Solution Steps

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

$$\frac{78000}{13}<\frac{78}{0.13}\text{ and }\frac{78}{0.13}<\frac{0.0078}{0.0000013}$$

Divide 78000 by 13 to get 6000.

$$6000<\frac{78}{0.13}\text{ and }\frac{78}{0.13}<\frac{0.0078}{0.0000013}$$

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

$$6000<\frac{7800}{13}\text{ and }\frac{78}{0.13}<\frac{0.0078}{0.0000013}$$

Divide 7800 by 13 to get 600.

$$6000<600\text{ and }\frac{78}{0.13}<\frac{0.0078}{0.0000013}$$

Compare 6000 and 600.

$$\text{false}\text{ and }\frac{78}{0.13}<\frac{0.0078}{0.0000013}$$

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

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

Divide 7800 by 13 to get 600.

$$\text{false}\text{ and }600<\frac{0.0078}{0.0000013}$$

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

$$\text{false}\text{ and }600<\frac{78000}{13}$$

Divide 78000 by 13 to get 6000.

$$\text{false}\text{ and }600<6000$$

Compare 600 and 6000.

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

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

$$\text{false}$$