Carry out the following conversions. (b) 8.5 cm^3 = _____ m^3 = _____ mm^3

Verified step by step guidance

1. Step 1: To convert from cubic centimeters (cm^3) to cubic meters (m^3), you need to know that 1 m^3 is equal to 1,000,000 cm^3. Therefore, to convert 8.5 cm^3 to m^3, you divide 8.5 by 1,000,000.
2. Step 2: To convert from cubic centimeters (cm^3) to cubic millimeters (mm^3), you need to know that 1 cm^3 is equal to 1,000 mm^3. Therefore, to convert 8.5 cm^3 to mm^3, you multiply 8.5 by 1,000.
3. Step 3: Carry out the calculations for each conversion without rounding until the final step to ensure accuracy.
4. Step 4: After calculating, make sure to include the correct units (m^3 for cubic meters and mm^3 for cubic millimeters) in your final answer.
5. Step 5: Finally, check your work to make sure your calculations and units are correct.

Key Concepts

Volume Units

Volume is a measure of the space occupied by a substance and is commonly expressed in various units such as cubic centimeters (cm³), cubic meters (m³), and cubic millimeters (mm³). Understanding the relationships between these units is essential for converting between them accurately.

Metric System Conversions

The metric system is a decimal-based system of measurement where units are related by powers of ten. For volume, 1 m³ equals 1,000,000 cm³ and 1 cm³ equals 1,000 mm³. Familiarity with these conversion factors allows for straightforward calculations when converting between different volume units.

Dimensional Analysis

Dimensional analysis is a mathematical technique used to convert one unit of measurement to another by multiplying by conversion factors. This method ensures that units cancel appropriately, leading to the desired unit in the final answer. It is a crucial skill in chemistry for performing accurate conversions.