Question

conversions and dimensional analysis practice
write the abbreviation for each metric unit.

1. kilogram
2. meter
3. gram
4. milliliter
5. millimeter
6. liter
7. kilometer
8. centimeter
9. milligram

complete these conversions using the ladder method.

1. 2000mg= g
2. 5l= ml
3. 16cm= mm
4. 104km= m
5. 198g= g
6. 50cm= m
7. 8mm= cm
8. 576l= kl
9. 97.62kg= g
10. which is larger?

a. 60,000g or 6kg
b. 1.28m or 128dm
c. 1kg+600g or 150,000g

1. add the following: 405mg, 0.500g, .002kg, 10dg. express your answer in grams.

dimensional analysis practice
for problems 1 - 3, please use dimensional analysis and these conversion factors:
pallet = 45 bundles 1 bundle = 32 cases 1 case = 12 cans 1 can = 218.4 ml

1. how many ml of apple juice does the company need to make to fulfill an order for 2.5 pallets?
2. if 46,680 ml of juice are produced, how many cases of juice can be made?
3. a certain store ordered 480 cases of juice. how many pallets were required to ship the order?

Explanation:

Step1: Write metric - unit abbreviations

1. Kilogram: kg
2. Meter: m
3. Gram: g
4. Milliliter: mL
5. Millimeter: mm
6. Liter: L
7. Kilometer: km
8. Centimeter: cm
9. Milligram: mg

Step2: Use the ladder - method for conversions

1. Since 1g = 1000mg, then 2000mg = 2000÷1000 = 2g
2. Since 1L = 1000mL, then 5L = 5×1000 = 5000mL
3. Since 1cm = 10mm, then 16cm = 16×10 = 160mm
4. Since 1km = 1000m, then 104km = 104×1000 = 104000m
5. 198g = 198g (no conversion needed)
6. Since 1m = 100cm, then 50cm = 50÷100 = 0.5m
7. Since 1cm = 10mm, then 8mm = 8÷10 = 0.8cm
8. Since 1kL = 1000L, then 576L = 576÷1000 = 0.576kL
9. Since 1kg = 1000g, then 97.62kg = 97.62×1000 = 97620g

Step3: Compare values

a. Since 1kg = 1000g, 6kg = 6×1000 = 6000g. So 60000g > 6kg
b. Since 1m = 10dm, 1.28m = 1.28×10 = 12.8dm. So 128dm > 1.28m
c. 1kg+600g = 1000g + 600g = 1600g. So 150000g > 1kg + 600g

Step4: Add values after conversion

405mg = 405÷1000 = 0.405g, 0.002kg = 0.002×1000 = 2g, 10dg = 10÷10 = 1g. Then 0.405g+0.500g + 2g+1g = 3.905g

Step5: Dimensional - analysis problems

1. For 2.5 pallets:

• First, find the number of bundles: 2.5 pallets×45 bundles/pallet = 112.5 bundles
• Then, find the number of cases: 112.5 bundles×32 cases/bundle = 3600 cases
• Then, find the number of cans: 3600 cases×12 cans/case = 43200 cans
• Then, find the volume in mL: 43200 cans×218.4mL/can = 9434880mL

1. If 46680mL of juice are produced:

• First, find the number of cans: 46680mL÷218.4mL/can = 213.74 cans (approx). Since we can't have a fraction of a can in a practical - sense, assume whole - number operations. Let's assume we are dealing with whole numbers of cans. 46680mL÷218.4mL/can = 213.74≈214 cans
• Then, find the number of cases: 214 cans÷12 cans/case≈17.83 cases. Rounding up, we get 18 cases

1. If there are 480 cases of juice:

• First, find the number of bundles: 480 cases÷32 cases/bundle = 15 bundles
• Then, find the number of pallets: 15 bundles÷45 bundles/pallet≈0.33 pallets. Rounding up, we get 1 pallet (if we can't have a fraction of a pallet for shipping)

Answer:

1. kg
2. m
3. g
4. mL
5. mm
6. L
7. km
8. cm
9. mg
10. 2g
11. 5000mL
12. 160mm
13. 104000m
14. 198g
15. 0.5m
16. 0.8cm
17. 0.576kL
18. 97620g
19. a. 60000g

b. 128dm
c. 150000g

1. 3.905g
2. 9434880mL
3. 18 cases
4. 1 pallet