To find the length of the chalkboard in decimeters (dm), we need to convert each measurement (meters, centimeters, millimeters) to decimeters and then sum them up. Here's the step-by-step solution:
1. Convert 3 meters to decimeters:
- Since 1 meter equals 10 decimeters, multiply the number of meters by 10.
- [tex]\( 3 \text{ meters} \times 10 = 30 \text{ decimeters} \)[/tex]
2. Convert 34 centimeters to decimeters:
- Since 1 decimeter equals 10 centimeters, divide the number of centimeters by 10.
- [tex]\( 34 \text{ centimeters} \div 10 = 3.4 \text{ decimeters} \)[/tex]
3. Convert 5 millimeters to decimeters:
- Since 1 decimeter equals 100 millimeters, divide the number of millimeters by 100.
- [tex]\( 5 \text{ millimeters} \div 100 = 0.05 \text{ decimeters} \)[/tex]
4. Add up all the converted measurements:
- Add the decimeters from each conversion: the meters, the centimeters, and the millimeters.
- [tex]\( 30 \text{ decimeters} + 3.4 \text{ decimeters} + 0.05 \text{ decimeters} = 33.449999999999996 \text{ decimeters} \)[/tex]
Therefore, the length of the chalkboard in decimeters is [tex]\( 33.45 \)[/tex] (rounded to 2 decimal places).
