Question

Rocks at Earth's surface have an average density of 3(g)/(c)m^(3). Can you convert this to k(g)/(k)m^(3)?1kg=1000g and 1km=100000cm. Write your answer in scientific notation.

Answer 1

The average density of Earth's surface rocks, initially given as 3 g/cm³, when converted to kg/km³ is 3 × 10¹ kg/km³.

Step-by-step explanation:

To convert from grams per cubic centimeter (g/cm³) to kilograms per cubic kilometer (kg/km³), we must factor in the conversions for grams to kilograms and centimeters to kilometers. Since 1 kilogram is equal to 1000 grams, and 1 kilometer is 100000 centimeters, we can set up the conversion as follows:

1. First, convert the mass from grams to kilograms: 3 g = 3 / 1000 kg = 0.003 kg.
2. Then, convert each dimension of the volume from centimeters to kilometers: (1 cm) ³ = (1/100000 km) ³ = 1 × 10⁻¹¹ km³.

Since density is mass per unit volume, the converted density is:

1. (0.003 kg) / (1 × 10⁻¹¹ km³) =
   
   0.003 kg / 1 × 10⁻¹µ km³ =
   
   3 × 10⁻³ kg / 1 × 10⁻µ km³ =
   
   3 × 10¹ km³

In scientific notation, the average density of Earth's surface rocks in kilograms per cubic kilometer is 3 × 10¹ kg/km³. Note that we use exponent rules to divide the values.