High School

Calculate the product:

[tex]9 \, \text{kg} \, 3 \, \text{hg} \, 1 \, \text{cg} \times 9[/tex]

Select one of the following options:

A. 83 kg 7 hg 9 cg
B. 75 kg 6 hg 8 cg
C. 67 kg 5 hg 2 cg
D. 91 kg 8 hg 4 cg

Answer :

Sure! Let's go through the problem step-by-step to determine the product of 9 kg 3 hg 1 cg multiplied by 9, expressed in kilograms (kg), hectograms (hg), and centigrams (cg).

1. Understand the Notations:
- kg stands for kilograms.
- hg stands for hectograms.
- cg stands for centigrams.

2. Convert Everything to Centigrams:
- Since 1 kg = 100,000 cg, 9 kg = 9 x 100,000 = 900,000 cg.
- Since 1 hg = 10,000 cg, 3 hg = 3 x 10,000 = 30,000 cg.
- 1 cg = 1 cg.

Therefore, the total centigrams initially = 900,000 + 30,000 + 1 = 930,001 cg.

3. Multiply by 9:
- Multiply the total centigrams by 9 to find the final amount in centigrams.
- So, 930,001 cg × 9 = 8,370,009 cg.

4. Convert Back to Mixed Units (kg, hg, cg):
- First, convert to kilograms: divide by 100,000 (since 1 kg = 100,000 cg).
- Kilograms (kg) = 8,370,009 // 100,000 = 83 kg.
- Remainder after kg = 8,370,009 % 100,000 = 70,009 cg.

- Next, convert the remainder to hectograms: divide by 10,000 (since 1 hg = 10,000 cg).
- Hectograms (hg) = 70,009 // 10,000 = 7 hg.
- Remainder after hg = 70,009 % 10,000 = 9 cg.

5. Final Result:
- After multiplication and converting back, we get:
- 83 kg 7 hg 9 cg.

The calculation corresponds to one of the answer choices: 83 kg 7 hg 9 cg.

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