Question

Maya is building a house in the shape of a rectangular prism for her cat. The house has a length of 1.2 × 10^3 mm, a width of 3.9 × 10^2 mm, and a height of 2.1 × 10^2 mm.

Find the volume of the house in scientific notation and in standard form. Answers should not be rounded.

The volume of the house written in scientific notation is a × 10^b cubic millimeters, where a is ____
and b is ____

The volume of the house written in standard form is ____
cubic millimeters.

Answer 1

Convert the scientific numbers to standard form:

1.2 x 10^3 = 1,200

3.9 x 10^2 = 390

2.1 x 10^2 = 210

Volume = 1200 x 390 x 210 = 98,280,000 cubic mm

Now convert standard form to scientific form by moving the c=decimal to the left and counting the number of spaces it moved.

Scientific notation:

98,280,000 = 9.828 x 10^7 ( a = 9.828 abd b = 7 )

Standard form:

98,280,000 cubic mm