The density of water is 1 g/cm3. Brent used the following method to convert 1 g/cm3 to kg/m3. An equation is shown. The expression on the left has three terms separated by the multiplication sign. The first term is 1 g by 1 cubic cm. The second term is 1 kg by 1000 kg. The third term is 100 cm raised to the power of 3 divided by 1 m raised to the power of 3. The number on the right of the equal to sign is 1000 kg per cubic meter. (1 kg = 1,000 g and 1 m = 100 cm) What is the error in Brent's conversion method?

The error includes;

a) The wrong denominator for the equivalent fraction of kilograms to grams

b) The use of the scale factor of length rather than the scale factor of volume for the equivalent fraction of cubic centimeters to cubic meters

c) The arrival at the correct 1000 kg/m³ rather than 0.1 g/m³ based on the expression on the left of the equation

Explanation:

The density of water = 1 g/cm³

The given equation is presented as follows;

1 g/cm³ × 1 kg/(1000 kg) × 100 cm³/(1 m³) = 1000 kg/m³

The error in the conversion method are;

a) The conversion, 1 kg/(1,000 kg) has an error, the correct conversion is (1 kg)/1,000 g)

b) The volume conversion error, 100 cm³/(1 m³), the correct volume conversion is (100 cm)³/(1 m³) = 1,000,000 cm³/(1 m³)

c) The right of the equal to sign error; using the left side expression only, the (wrong) answer is 0.1 g/m³

The correct equation is presented as follows;

1 g/cm³ × 1 kg/(1000 g) × 1,000,000 cm³/(1 m³) = 1000 kg/m³

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