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Answer :
To solve the problem of multiplying the quantity [tex]\(9 \, \text{kg} \, 3 \, \text{hg} \, 1 \, \text{cg}\)[/tex] by 9, follow these steps:
1. Understand the Units and Convert to Grams:
- Kilograms (kg): 1 kg = 1000 grams
- Hectograms (hg): 1 hg = 100 grams
- Centigrams (cg): 1 cg = 0.01 grams
Now, convert each unit into grams:
- For 9 kg: [tex]\(9 \times 1000 = 9000\)[/tex] grams
- For 3 hg: [tex]\(3 \times 100 = 300\)[/tex] grams
- For 1 cg: [tex]\(1 \times 0.01 = 0.01\)[/tex] grams
2. Find Total Grams Initially:
Add the converted values to get the total initial amount in grams:
[tex]\[
9000 + 300 + 0.01 = 9300.01 \text{ grams}
\][/tex]
3. Multiply by 9:
Compute the product by multiplying the total grams by 9:
[tex]\[
9300.01 \times 9 = 83700.09 \text{ grams}
\][/tex]
4. Convert Back to Kilograms, Hectograms, and Centigrams:
- Kilograms: Divide the total grams by 1000 to get kilograms:
[tex]\[
83700.09 \div 1000 = 83 \text{ kg} \text{ (and remainder 700.09 grams)}
\][/tex]
- Hectograms: From the remainder, divide by 100:
[tex]\[
700.09 \div 100 = 7 \text{ hg} \text{ (and remainder 0.09 grams)}
\][/tex]
- Centigrams: The remainder in grams is then 0.09, which in centigrams is:
[tex]\[
0.09 \div 0.01 = 9 \text{ cg}
\][/tex]
5. Conclusion:
Therefore, the final answer is [tex]\(83 \, \text{kg} \, 7 \, \text{hg} \, 9 \, \text{cg}\)[/tex].
Thus, the correct option is: 83 kg 7 hg 9 cg.
1. Understand the Units and Convert to Grams:
- Kilograms (kg): 1 kg = 1000 grams
- Hectograms (hg): 1 hg = 100 grams
- Centigrams (cg): 1 cg = 0.01 grams
Now, convert each unit into grams:
- For 9 kg: [tex]\(9 \times 1000 = 9000\)[/tex] grams
- For 3 hg: [tex]\(3 \times 100 = 300\)[/tex] grams
- For 1 cg: [tex]\(1 \times 0.01 = 0.01\)[/tex] grams
2. Find Total Grams Initially:
Add the converted values to get the total initial amount in grams:
[tex]\[
9000 + 300 + 0.01 = 9300.01 \text{ grams}
\][/tex]
3. Multiply by 9:
Compute the product by multiplying the total grams by 9:
[tex]\[
9300.01 \times 9 = 83700.09 \text{ grams}
\][/tex]
4. Convert Back to Kilograms, Hectograms, and Centigrams:
- Kilograms: Divide the total grams by 1000 to get kilograms:
[tex]\[
83700.09 \div 1000 = 83 \text{ kg} \text{ (and remainder 700.09 grams)}
\][/tex]
- Hectograms: From the remainder, divide by 100:
[tex]\[
700.09 \div 100 = 7 \text{ hg} \text{ (and remainder 0.09 grams)}
\][/tex]
- Centigrams: The remainder in grams is then 0.09, which in centigrams is:
[tex]\[
0.09 \div 0.01 = 9 \text{ cg}
\][/tex]
5. Conclusion:
Therefore, the final answer is [tex]\(83 \, \text{kg} \, 7 \, \text{hg} \, 9 \, \text{cg}\)[/tex].
Thus, the correct option is: 83 kg 7 hg 9 cg.
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