Question

What conversion factors would be used to convert grams per day to kilograms per week

Answer 1

• (1 kg)/(1000 g)
• (7 day)/(1 wk)

Explanation:

You want to know the conversion factors that would be used to convert grams per day to kilograms per week.

Conversion factors

A conversion factor is often expressed as a ratio that has its numerator equal to its denominator, but expressed with different units. The units of a conversion factor are generally chosen to be useful for the purpose of converting units you have to units you want.

Application

Here, we have mass units of grams, and we want mass units of kilograms. We know that ...

1000 g = 1 kg

so a suitable conversion factor is ...

(1 kg)/(1000 g)

The units we have (g) are put in the denominator, so that multiplying by this factor will cancel units of grams, leaving units of kilograms.

We have time units of days, and we want time units of weeks. The time units are in the denominator of the original value (g/day). We know that ...

7 day = 1 wk

so a suitable conversion factor is ...

(7 day)/(1 wk)

The time unit of day in the numerator will cancel the time unit of day in the original value, leaving time units of weeks in the denominator.

`1\frac{\text{g}}{\text{day}}=1\frac{\text{g}}{\text{day}}\cdot\boxed{\frac{1\text{ kg}}{1000\text{ g}}\cdot\frac{7\text{ day}}{1\text{ wk}}}=\frac{7\text{ kg}}{1000\text{ wk}}=0.007\text{ kg/wk}`