Clear and organized math worksheet designed to help students practice converting metric units of length, mass, and volume.
Metric Conversion Worksheet 2 with 20 problems converting units using the ladder method.
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Step-by-step solution for: Metric Conversion Worksheet 2 | Study notes Physics | Docsity
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Show Answer Key & Explanations
Step-by-step solution for: Metric Conversion Worksheet 2 | Study notes Physics | Docsity
Here are the solutions to the metric conversion problems. To solve these, we move the decimal point based on the "ladder" of metric units:
The Ladder:
* Kilo (k)
* Hecto (h)
* Deca (da)
* Base Unit (meter, liter, gram)
* Deci (d)
* Centi (c)
* Milli (m)
Rule:
* Going down the ladder (e.g., km to m): Move decimal to the right.
* Going up the ladder (e.g., mm to m): Move decimal to the left.
***
1. 11.5 dag = \_\_\_\_\_ cg
* From Deca (dag) to Centi (cg): Down 3 steps (da $\rightarrow$ base $\rightarrow$ d $\rightarrow$ c).
* Move decimal right 3 spots: $11.5 \rightarrow 115 \rightarrow 1150 \rightarrow 11500$.
* Answer: 11,500
2. 99,000 mm = \_\_\_\_\_ dam
* From Milli (mm) to Deca (dam): Up 4 steps (m $\rightarrow$ d $\rightarrow$ base $\rightarrow$ da).
* Move decimal left 4 spots: $99000. \rightarrow 9900. \rightarrow 990. \rightarrow 99. \rightarrow 9.9$.
* Answer: 9.9
3. 260,000 mm = \_\_\_\_\_ hm
* From Milli (mm) to Hecto (hm): Up 5 steps (m $\rightarrow$ d $\rightarrow$ base $\rightarrow$ da $\rightarrow$ h).
* Move decimal left 5 spots: $260000. \rightarrow 26000. \rightarrow 2600. \rightarrow 260. \rightarrow 26. \rightarrow 2.6$.
* Answer: 2.6
4. 20 mm = \_\_\_\_\_ dm
* From Milli (mm) to Deci (dm): Up 1 step.
* Move decimal left 1 spot: $20. \rightarrow 2.0$.
* Answer: 2
5. 33,000 mm = \_\_\_\_\_ dam
* From Milli (mm) to Deca (dam): Up 4 steps.
* Move decimal left 4 spots: $33000. \rightarrow 3300. \rightarrow 330. \rightarrow 33. \rightarrow 3.3$.
* Answer: 3.3
6. 1,150 mg = \_\_\_\_\_ dg
* From Milli (mg) to Deci (dg): Up 2 steps (m $\rightarrow$ d). *Note: The unit is decigram.*
* Move decimal left 2 spots: $1150. \rightarrow 115. \rightarrow 11.5$.
* Answer: 11.5
7. 77,000 ml = \_\_\_\_\_ dal
* From Milli (ml) to Deca (dal): Up 4 steps.
* Move decimal left 4 spots: $77000. \rightarrow 7700. \rightarrow 770. \rightarrow 77. \rightarrow 7.7$.
* Answer: 7.7
8. 640 dm = \_\_\_\_\_ dam
* From Deci (dm) to Deca (dam): Up 2 steps (d $\rightarrow$ base $\rightarrow$ da).
* Move decimal left 2 spots: $640. \rightarrow 64. \rightarrow 6.4$.
* Answer: 6.4
9. 2,680 dl = \_\_\_\_\_ dal
* From Deci (dl) to Deca (dal): Up 2 steps.
* Move decimal left 2 spots: $2680. \rightarrow 268. \rightarrow 26.8$.
* Answer: 26.8
10. 10 m = \_\_\_\_\_ dam
* From Base (m) to Deca (dam): Up 1 step.
* Move decimal left 1 spot: $10. \rightarrow 1.0$.
* Answer: 1
11. 10.4 hl = \_\_\_\_\_ dl
* From Hecto (hl) to Deci (dl): Down 3 steps (h $\rightarrow$ da $\rightarrow$ base $\rightarrow$ d).
* Move decimal right 3 spots: $10.4 \rightarrow 104 \rightarrow 1040 \rightarrow 10400$.
* Answer: 10,400
12. 0.1 cm = \_\_\_\_\_ mm
* From Centi (cm) to Milli (mm): Down 1 step.
* Move decimal right 1 spot: $0.1 \rightarrow 1$.
* Answer: 1
13. 300 dm = \_\_\_\_\_ dam
* From Deci (dm) to Deca (dam): Up 2 steps.
* Move decimal left 2 spots: $300. \rightarrow 30. \rightarrow 3$.
* Answer: 3
14. 1,900 dl = \_\_\_\_\_ hl
* From Deci (dl) to Hecto (hl): Up 3 steps (d $\rightarrow$ base $\rightarrow$ da $\rightarrow$ h).
* Move decimal left 3 spots: $1900. \rightarrow 190. \rightarrow 19. \rightarrow 1.9$.
* Answer: 1.9
15. 34.4 hm = \_\_\_\_\_ dam
* From Hecto (hm) to Deca (dam): Down 1 step.
* Move decimal right 1 spot: $34.4 \rightarrow 344$.
* Answer: 344
16. 8.4 g = \_\_\_\_\_ mg
* From Base (g) to Milli (mg): Down 3 steps (base $\rightarrow$ d $\rightarrow$ c $\rightarrow$ m).
* Move decimal right 3 spots: $8.4 \rightarrow 84 \rightarrow 840 \rightarrow 8400$.
* Answer: 8,400
17. 6 L = \_\_\_\_\_ dal
* From Base (L) to Deca (dal): Up 1 step.
* Move decimal left 1 spot: $6. \rightarrow 0.6$.
* Answer: 0.6
18. 9.3 dam = \_\_\_\_\_ dm
* From Deca (dam) to Deci (dm): Down 2 steps (da $\rightarrow$ base $\rightarrow$ d).
* Move decimal right 2 spots: $9.3 \rightarrow 93 \rightarrow 930$.
* Answer: 930
19. 10.8 hg = \_\_\_\_\_ cg
* From Hecto (hg) to Centi (cg): Down 4 steps (h $\rightarrow$ da $\rightarrow$ base $\rightarrow$ d $\rightarrow$ c).
* Move decimal right 4 spots: $10.8 \rightarrow 108 \rightarrow 1080 \rightarrow 10800 \rightarrow 108000$.
* Answer: 108,000
20. 9.7 dm = \_\_\_\_\_ mm
* From Deci (dm) to Milli (mm): Down 2 steps (d $\rightarrow$ c $\rightarrow$ m).
* Move decimal right 2 spots: $9.7 \rightarrow 97 \rightarrow 970$.
* Answer: 970
Final Answer:
1. 11,500
2. 9.9
3. 2.6
4. 2
5. 3.3
6. 11.5
7. 7.7
8. 6.4
9. 26.8
10. 1
11. 10,400
12. 1
13. 3
14. 1.9
15. 344
16. 8,400
17. 0.6
18. 930
19. 108,000
20. 970
The Ladder:
* Kilo (k)
* Hecto (h)
* Deca (da)
* Base Unit (meter, liter, gram)
* Deci (d)
* Centi (c)
* Milli (m)
Rule:
* Going down the ladder (e.g., km to m): Move decimal to the right.
* Going up the ladder (e.g., mm to m): Move decimal to the left.
***
1. 11.5 dag = \_\_\_\_\_ cg
* From Deca (dag) to Centi (cg): Down 3 steps (da $\rightarrow$ base $\rightarrow$ d $\rightarrow$ c).
* Move decimal right 3 spots: $11.5 \rightarrow 115 \rightarrow 1150 \rightarrow 11500$.
* Answer: 11,500
2. 99,000 mm = \_\_\_\_\_ dam
* From Milli (mm) to Deca (dam): Up 4 steps (m $\rightarrow$ d $\rightarrow$ base $\rightarrow$ da).
* Move decimal left 4 spots: $99000. \rightarrow 9900. \rightarrow 990. \rightarrow 99. \rightarrow 9.9$.
* Answer: 9.9
3. 260,000 mm = \_\_\_\_\_ hm
* From Milli (mm) to Hecto (hm): Up 5 steps (m $\rightarrow$ d $\rightarrow$ base $\rightarrow$ da $\rightarrow$ h).
* Move decimal left 5 spots: $260000. \rightarrow 26000. \rightarrow 2600. \rightarrow 260. \rightarrow 26. \rightarrow 2.6$.
* Answer: 2.6
4. 20 mm = \_\_\_\_\_ dm
* From Milli (mm) to Deci (dm): Up 1 step.
* Move decimal left 1 spot: $20. \rightarrow 2.0$.
* Answer: 2
5. 33,000 mm = \_\_\_\_\_ dam
* From Milli (mm) to Deca (dam): Up 4 steps.
* Move decimal left 4 spots: $33000. \rightarrow 3300. \rightarrow 330. \rightarrow 33. \rightarrow 3.3$.
* Answer: 3.3
6. 1,150 mg = \_\_\_\_\_ dg
* From Milli (mg) to Deci (dg): Up 2 steps (m $\rightarrow$ d). *Note: The unit is decigram.*
* Move decimal left 2 spots: $1150. \rightarrow 115. \rightarrow 11.5$.
* Answer: 11.5
7. 77,000 ml = \_\_\_\_\_ dal
* From Milli (ml) to Deca (dal): Up 4 steps.
* Move decimal left 4 spots: $77000. \rightarrow 7700. \rightarrow 770. \rightarrow 77. \rightarrow 7.7$.
* Answer: 7.7
8. 640 dm = \_\_\_\_\_ dam
* From Deci (dm) to Deca (dam): Up 2 steps (d $\rightarrow$ base $\rightarrow$ da).
* Move decimal left 2 spots: $640. \rightarrow 64. \rightarrow 6.4$.
* Answer: 6.4
9. 2,680 dl = \_\_\_\_\_ dal
* From Deci (dl) to Deca (dal): Up 2 steps.
* Move decimal left 2 spots: $2680. \rightarrow 268. \rightarrow 26.8$.
* Answer: 26.8
10. 10 m = \_\_\_\_\_ dam
* From Base (m) to Deca (dam): Up 1 step.
* Move decimal left 1 spot: $10. \rightarrow 1.0$.
* Answer: 1
11. 10.4 hl = \_\_\_\_\_ dl
* From Hecto (hl) to Deci (dl): Down 3 steps (h $\rightarrow$ da $\rightarrow$ base $\rightarrow$ d).
* Move decimal right 3 spots: $10.4 \rightarrow 104 \rightarrow 1040 \rightarrow 10400$.
* Answer: 10,400
12. 0.1 cm = \_\_\_\_\_ mm
* From Centi (cm) to Milli (mm): Down 1 step.
* Move decimal right 1 spot: $0.1 \rightarrow 1$.
* Answer: 1
13. 300 dm = \_\_\_\_\_ dam
* From Deci (dm) to Deca (dam): Up 2 steps.
* Move decimal left 2 spots: $300. \rightarrow 30. \rightarrow 3$.
* Answer: 3
14. 1,900 dl = \_\_\_\_\_ hl
* From Deci (dl) to Hecto (hl): Up 3 steps (d $\rightarrow$ base $\rightarrow$ da $\rightarrow$ h).
* Move decimal left 3 spots: $1900. \rightarrow 190. \rightarrow 19. \rightarrow 1.9$.
* Answer: 1.9
15. 34.4 hm = \_\_\_\_\_ dam
* From Hecto (hm) to Deca (dam): Down 1 step.
* Move decimal right 1 spot: $34.4 \rightarrow 344$.
* Answer: 344
16. 8.4 g = \_\_\_\_\_ mg
* From Base (g) to Milli (mg): Down 3 steps (base $\rightarrow$ d $\rightarrow$ c $\rightarrow$ m).
* Move decimal right 3 spots: $8.4 \rightarrow 84 \rightarrow 840 \rightarrow 8400$.
* Answer: 8,400
17. 6 L = \_\_\_\_\_ dal
* From Base (L) to Deca (dal): Up 1 step.
* Move decimal left 1 spot: $6. \rightarrow 0.6$.
* Answer: 0.6
18. 9.3 dam = \_\_\_\_\_ dm
* From Deca (dam) to Deci (dm): Down 2 steps (da $\rightarrow$ base $\rightarrow$ d).
* Move decimal right 2 spots: $9.3 \rightarrow 93 \rightarrow 930$.
* Answer: 930
19. 10.8 hg = \_\_\_\_\_ cg
* From Hecto (hg) to Centi (cg): Down 4 steps (h $\rightarrow$ da $\rightarrow$ base $\rightarrow$ d $\rightarrow$ c).
* Move decimal right 4 spots: $10.8 \rightarrow 108 \rightarrow 1080 \rightarrow 10800 \rightarrow 108000$.
* Answer: 108,000
20. 9.7 dm = \_\_\_\_\_ mm
* From Deci (dm) to Milli (mm): Down 2 steps (d $\rightarrow$ c $\rightarrow$ m).
* Move decimal right 2 spots: $9.7 \rightarrow 97 \rightarrow 970$.
* Answer: 970
Final Answer:
1. 11,500
2. 9.9
3. 2.6
4. 2
5. 3.3
6. 11.5
7. 7.7
8. 6.4
9. 26.8
10. 1
11. 10,400
12. 1
13. 3
14. 1.9
15. 344
16. 8,400
17. 0.6
18. 930
19. 108,000
20. 970
Parent Tip: Review the logic above to help your child master the concept of metric conversions chemistry worksheet.
