Metric Conversions: decimeter one tenth of a meter, centimeter one hundredth of a meter, millimeter one thousandth of a meter, 1000 mm = 100 cm = 10 dm = 1 m. Compare these measurements, using or =: 1) 100 mm 1 dm 2) 1 cm = 10 mm 3) 1 dm = 100 mm 4) 1 cm = 10 mm Convert and calculate: a) 6 m 3 dm 2 cm + 2 m 74 cm = cm cm = cm b) 3 m 4 dm – 12 dm 5 cm = cm cm = cm c) 8 dm 2 cm – 3 dm 4 cm = cm cm = cm d) 1 m 92 cm + 59 dm = cm cm = cm
The Correct Answer and Explanation is:
Answers to Metric Comparisons
- 100 mm < 1 dm (since 1 dm = 100 mm)
- 1 cm = 10 mm (1 cm is exactly 10 mm)
- 1 dm = 100 mm (1 dm is equal to 100 mm)
- 1 cm = 10 mm (same as 2nd comparison)
Conversion and Calculation
a) 6 m 3 dm 2 cm + 2 m 74 cm
- Convert everything to centimeters:
- 6 m = 600 cm
- 3 dm = 30 cm
- 2 cm = 2 cm
- 2 m = 200 cm
- 74 cm remains 74 cm
- Addition: 600 + 30 + 2 + 200 + 74 = 906 cm
b) 3 m 4 dm – 12 dm 5 cm
- Convert everything to centimeters:
- 3 m = 300 cm
- 4 dm = 40 cm
- 12 dm = 120 cm
- 5 cm remains 5 cm
- Subtraction: (300 + 40) – (120 + 5) = 340 – 125 = 215 cm
c) 8 dm 2 cm – 3 dm 4 cm
- Convert everything to centimeters:
- 8 dm = 80 cm
- 2 cm remains 2 cm
- 3 dm = 30 cm
- 4 cm remains 4 cm
- Subtraction: (80 + 2) – (30 + 4) = 82 – 34 = 48 cm
d) 1 m 92 cm + 59 dm
- Convert everything to centimeters:
- 1 m = 100 cm
- 92 cm remains 92 cm
- 59 dm = 590 cm
- Addition: 100 + 92 + 590 = 782 cm
Explanation of the Approach
Metric conversions simplify calculations by expressing all quantities in the same unit before performing operations. This method ensures precision and consistency. When dealing with conversions, each unit must be transformed correctly:
- Meters convert to centimeters by multiplying by 100.
- Decimeters convert to centimeters by multiplying by 10.
- Millimeters convert to centimeters by dividing by 10.
For addition, individual values are converted and summed systematically. In subtraction, values are converted and then calculated accordingly. These principles support accurate measurement adjustments and real-world applications such as engineering, physics, and chemistry, where consistent units are required for precision.
