Metric Units of Length (mm, cm, m, km): Fifth Grade Mathematics

Metric length measurements scale from microscopic millimeters to expansive kilometers using decimal point shifts.

Common Metric Length Units

In fifth grade, the four primary metric units of length are:
- Millimeter (mm): Thickness of a plastic ID card or pencil tip (1 mm = 0.001 m).

- Centimeter (cm): Width of a fingertip or paperclip (1 cm = 0.01 m = 10 mm).

- Meter (m): Width of a doorway or height of a desk (1 m = 100 cm = 1,000 mm).

- Kilometer (km): Six city blocks or a little over half a mile (1 km = 1,000 m).

+--------------------------------------------------------------------------+
|                  METRIC LENGTH CONVERSIONS                               |
+---------------------+----------------------------+-----------------------+
| Smaller Unit        | Equivalence                | Larger Unit           |
+---------------------+----------------------------+-----------------------+
| Millimeters (mm)    | 10 mm                      | = 1 centimeter (cm)   |
| Centimeters (cm)    | 100 cm                     | = 1 meter (m)         |
| Millimeters (mm)    | 1,000 mm                   | = 1 meter (m)         |
| Meters (m)          | 1,000 m                    | = 1 kilometer (km)    |
+---------------------+----------------------------+-----------------------+

Converting Metric Lengths via Decimal Shifts

Because metric conversions are powers of 10, converting simply shifts the decimal point:
- Meters to Centimeters: Multiply by 100 (shift decimal 2 places RIGHT). E.g., 3.4 m = 340 cm.

- Centimeters to Meters: Divide by 100 (shift decimal 2 places LEFT). E.g., 785 cm = 7.85 m.

- Kilometers to Meters: Multiply by 1,000 (shift decimal 3 places RIGHT). E.g., 0.85 km = 850 m.

- Millimeters to Centimeters: Divide by 10 (shift decimal 1 place LEFT). E.g., 42 mm = 4.2 cm.

Exercises and Solutions

Exercise 1: Metric Length Conversions. Convert the following measurements: Part A: Convert 6.2 kilometers into meters. Part B: Convert 385 millimeters into centimeters. Part C: Convert 42 centimeters into meters.

Solution 1: For Part A: Converting km to m requires multiplying by 1,000 (shift decimal 3 places right): 6.2 * 1,000 = 6,200 meters. For Part B: Converting mm to cm requires dividing by 10 (shift decimal 1 place left): 385 / 10 = 38.5 centimeters. For Part C: Converting cm to m requires dividing by 100 (shift decimal 2 places left): 42 / 100 = 0.42 meters.

Exercise 2: Track Relay Word Problem. A track runner participates in a 4-leg relay race where each leg is 400 meters long. How many kilometers did the runner's team complete in total?

Solution 2: First, find total distance in meters: 4 legs * 400 meters = 1,600 meters. Next, convert meters to kilometers: divide by 1,000 (shift decimal 3 places left): 1,600 / 1,000 = 1.6 kilometers. The team completed 1.6 kilometers.