Q62E - Chemistry (OpenStax)

Question

A woman's basketball has a circumference between 28.5 and 29.0 inches and a maximum weight of 20 ounces(two significant figures). What are these specifications in units of centimeters and grams?

Step-by-Step Solution

Answer

The circumference and weight in units of centimeters and grams are between 72 and 74cm and 570 grams.

Step 1: Converting the magnitude of circumference in a unit from inch to cm

We know that

\(1\,\,{\rm{inch}}\, = \,2.54\,\,{\rm{cm}}\)\[\]

For conversion in a unit from inch to cm,

\(\begin{aligned}{\underline{\phantom{xx}}}28.5\,\,inch\, = \,28.5\,(1\,inch)\, = \,28.5\,\, \times \,2.54\, = \,72.39\, \approx \,72\,cm\\29.0\,\,inch\, = \,29.0\,(1\,inch)\, = \,29.0\,\, \times \,2.54\, = \,73.66\, \approx \,74\,cm\end{aligned}\)

Hence, the circumference of the woman`s basketball in a unit of centimeters is between 72 and 74 cm in up to two significant figures.

Step 2: Converting the magnitude of weight in a unit from ounce to gm

Here,

\(1\,\,ounce\, = \,28.3495\,\,grams\)

For conversion in a unit from an ounce to gm,

\(\begin{aligned}{\underline{\phantom{xx}}}20\,\,ounce\, = \,20\,\,\left( {ounce\, \times \,\frac{g}{g}\,} \right) = \,20\, \times \,28.3495\,\,g\,\, = \,566.99\,\,g\\\, \approx \,\,567\,g\end{aligned}\)

Therefore, the magnitude of weight in a unit from ounce to gm is 567 grams in up to two significant figures.