Question

The label on a box of cereal gives the mass of cereal in two units: 978 grams and 34.5 oz. Use this information to find a conversion factor between the English and metric units. How many significant figures can you justify in your conversion factor?

978g:34.5oz
a) 978g:1000g
b) 978g:34.5oz
c) 978g:1000oz
d) 978g:34.50oz

Answer 1

The conversion factor from grams to ounces using the cereal box information b) (978 g and 34.5 oz) is 28.3 g/oz (rounded to three significant figures).

Step-by-step explanation:

To find a conversion factor between grams and ounces, we use the information that 978 grams is equal to 34.5 oz. From the relationship provided, we understand that 1 oz is equivalent to 28.35 g. Therefore, the conversion factor would be 978 g / 34.5 oz, which simplifies to 28.35 g / oz. When deciding the number of significant figures to justify in our conversion factor, we look at the original data provided, which has three significant figures for both grams and ounces; hence, the conversion factor should also reflect three significant figures, 28.3 g/oz.

To confirm this, we convert 34.5 oz to grams using the conversion factor of 1 oz = 28.35 g:

34.5 oz × 28.35 g/oz = 978.075 g ≈ 978 g (rounded to three significant figures, which the original measurement had).