In order to complete this conversion we have to know that there are  per . So this problem can be solved by dividing our  by , or moving the decimal place to the left by .

In order to complete this conversion we have to know that there are  per . So this problem can be solved by multiplying our  by , or moving the decimal place to the right by .

There are a total of 12 inches in one foot.

Write the dimensional analysis for the conversion.

Reduce the fraction.

The answer is:  

If we have an equation or expression or value such as the mass given in grams and we want to multiply it by something, we can multiply it by  and it will not change anything. When you convert units you are actually multiplying the value by . For example,

Since we are saying that one kilogram is equal to one thousand grams, we can divide both sides by  and get

Even though the units are different, we are still saying that since they are equal the above expression is true. Likewise we can flip the equation and it will still equal one,

We can use either of these, but our goal is to multiply our mass in grams by  and cancel the appropriate units. Let's try this:

Ok, that didn't turn out how we want it. We need to cancel  and have  left over. Let's try the second expression,

See how the grams cancel out and we are left with kilograms on the top? So we multiplied the value of the mass by  and made sure the units we didn't want canceled and we were left with the appropriate units.

Reconvert the hour into minutes.  There are 60 minutes in an hour.

Set up a proportion so that we can find how many miles Richard has traveled.

Cross multiply. 

Divide by 60 on both sides.

Simplify both sides.

Richard would have traveled five miles.

In order to convert from inches to yards, we will need to know the dimensional conversion from inches to feet, and from feet to yards.

There are 12 inches in a foot, and there are 3 feet in a yard.

Set up a dimensional analysis to convert the dimensions.

The inches and feet dimensions will cancel, leaving us with yards as the final unit.

Simplify the expression.

Write the conversion relating miles and inches.  The map is drawn where one mile is traveled per quarter inch marked.

Rewrite 3.75 into a fraction.

Multiply this dimension with the conversion to determine how many miles is the certain location. 

The inches unit will cancel, and will leave us with the mile unit.  Multiply the numerator with the numerator and the denominator with the denominator.

The location is 15 miles away.

There are  in . Write the conversion factor. The feet should be on the bottom since we will be multiplying the  with this conversion factor.

Multiply the  with this conversion factor to get the dimension in yards.

To convert from one measurement to another simply multiply or divide by all the measurements in between. Notice how each successive fraction has a denominator that cancels with the previous fraction so that we are finally left with just the measurement we want. Be careful to make sure the that you always write a correct ratio. 

There are sixty minutes in an hour, and sixty seconds in a minute.  We need to find the conversion from hours to seconds. 

Since seconds per hour will be the primary unit, write the dimensional analysis to do this conversion.

Multiply  hours with this conversion factor.

The answer is .