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Sagot :
Alright, let's tackle this problem step-by-step to find which of the given metric units is closest in weight to 1 pound.
### Step 1: Understand the Conversion Factors
First, let's establish the relevant metric conversions for 1 pound:
1 pound = 453.592 grams
Using this information, we can convert 1 pound into other metric units:
- Centigrams: There are 100 centigrams in a gram.
[tex]\( 453.592 \text{ grams} \times 100 = 45,359.2 \text{ centigrams} \)[/tex]
- Kilograms: There are 1000 grams in a kilogram.
[tex]\( 453.592 \text{ grams} \div 1000 = 0.453592 \text{ kilograms} \)[/tex]
- Milligrams: There are 1000 milligrams in a gram.
[tex]\( 453.592 \text{ grams} \times 1000 = 453,592 \text{ milligrams} \)[/tex]
### Step 2: Compare Conversions with Given Options
Now, let's compare these conversions with the given options:
1. 450 grams:
- Difference from 453.592 grams:
[tex]\( |453.592 - 450| = 3.592 \text{ grams} \)[/tex]
2. 4,500 centigrams:
- 4,500 centigrams converted to grams:
[tex]\( 4,500 \text{ centigrams} \div 100 = 45 \text{ grams} \)[/tex]
- Difference from 453.592 grams:
[tex]\( |453.592 - 45| = 408.592 \text{ grams} \)[/tex]
3. 0.045 kilograms:
- 0.045 kilograms converted to grams:
[tex]\( 0.045 \text{ kilograms} \times 1000 = 45 \text{ grams} \)[/tex]
- Difference from 453.592 grams:
[tex]\( |453.592 - 45| = 408.592 \text{ grams} \)[/tex]
4. 45,000 milligrams:
- 45,000 milligrams converted to grams:
[tex]\( 45,000 \text{ milligrams} \div 1000 = 45 \text{ grams} \)[/tex]
- Difference from 453.592 grams:
[tex]\( |453.592 - 45| = 408.592 \text{ grams} \)[/tex]
### Step 3: Identify the Closest Value
Compare the differences:
- 450 grams: 3.592 grams difference
- 4,500 centigrams (converted to 45 grams): 408.592 grams difference
- 0.045 kilograms (converted to 45 grams): 408.592 grams difference
- 45,000 milligrams (converted to 45 grams): 408.592 grams difference
The smallest difference is 3.592 grams with the option 450 grams.
### Conclusion
1 pound is closest in weight to 450 grams.
### Step 1: Understand the Conversion Factors
First, let's establish the relevant metric conversions for 1 pound:
1 pound = 453.592 grams
Using this information, we can convert 1 pound into other metric units:
- Centigrams: There are 100 centigrams in a gram.
[tex]\( 453.592 \text{ grams} \times 100 = 45,359.2 \text{ centigrams} \)[/tex]
- Kilograms: There are 1000 grams in a kilogram.
[tex]\( 453.592 \text{ grams} \div 1000 = 0.453592 \text{ kilograms} \)[/tex]
- Milligrams: There are 1000 milligrams in a gram.
[tex]\( 453.592 \text{ grams} \times 1000 = 453,592 \text{ milligrams} \)[/tex]
### Step 2: Compare Conversions with Given Options
Now, let's compare these conversions with the given options:
1. 450 grams:
- Difference from 453.592 grams:
[tex]\( |453.592 - 450| = 3.592 \text{ grams} \)[/tex]
2. 4,500 centigrams:
- 4,500 centigrams converted to grams:
[tex]\( 4,500 \text{ centigrams} \div 100 = 45 \text{ grams} \)[/tex]
- Difference from 453.592 grams:
[tex]\( |453.592 - 45| = 408.592 \text{ grams} \)[/tex]
3. 0.045 kilograms:
- 0.045 kilograms converted to grams:
[tex]\( 0.045 \text{ kilograms} \times 1000 = 45 \text{ grams} \)[/tex]
- Difference from 453.592 grams:
[tex]\( |453.592 - 45| = 408.592 \text{ grams} \)[/tex]
4. 45,000 milligrams:
- 45,000 milligrams converted to grams:
[tex]\( 45,000 \text{ milligrams} \div 1000 = 45 \text{ grams} \)[/tex]
- Difference from 453.592 grams:
[tex]\( |453.592 - 45| = 408.592 \text{ grams} \)[/tex]
### Step 3: Identify the Closest Value
Compare the differences:
- 450 grams: 3.592 grams difference
- 4,500 centigrams (converted to 45 grams): 408.592 grams difference
- 0.045 kilograms (converted to 45 grams): 408.592 grams difference
- 45,000 milligrams (converted to 45 grams): 408.592 grams difference
The smallest difference is 3.592 grams with the option 450 grams.
### Conclusion
1 pound is closest in weight to 450 grams.
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