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Answer :
To find out how many pebbles are in 45,284 grams, follow these steps:
1. Understand the problem:
- We know that 124 pebbles have a combined mass of 1.000 kg.
- We need to find how many pebbles correspond to a mass of 45,284 grams.
2. Convert the given mass to the same unit:
- The mass of 124 pebbles is given as 1.000 kg. We need to convert this to grams for easier calculations.
- 1 kg = 1,000 grams.
- Therefore, [tex]\( 1.000 \, \text{kg} = 1,000 \, \text{grams} = 1,000 \, \text{g} \)[/tex].
3. Calculate the mass of one pebble:
- We have 124 pebbles that weigh 1,000 grams.
- To find the mass of a single pebble, we divide the total mass by the number of pebbles.
- Mass of one pebble [tex]\[\text{(in grams)} = \frac{1,000 \, \text{grams}}{124 \, \text{pebbles}} \approx 8.065 \, \text{grams} \][/tex].
4. Calculate the number of pebbles in 45,284 grams:
- Now, we need to find out how many pebbles are there in 45,284 grams.
- We use the mass of one pebble calculated in the previous step.
- Number of pebbles = [tex]\[\frac{45,284 \, \text{grams}}{8.065 \, \text{grams/pebble}} \approx 5615.216 \, \text{pebbles} \][/tex].
5. Round to a reasonable number of significant figures:
- The number of pebbles is approximately 5615.216.
- Since we cannot have a fraction of a pebble, we can round this to the nearest whole number.
- Therefore, there are approximately [tex]\( 5615 \)[/tex] pebbles in 45,284 grams.
Thus, in 45,284 grams, there are approximately 5615 pebbles.
1. Understand the problem:
- We know that 124 pebbles have a combined mass of 1.000 kg.
- We need to find how many pebbles correspond to a mass of 45,284 grams.
2. Convert the given mass to the same unit:
- The mass of 124 pebbles is given as 1.000 kg. We need to convert this to grams for easier calculations.
- 1 kg = 1,000 grams.
- Therefore, [tex]\( 1.000 \, \text{kg} = 1,000 \, \text{grams} = 1,000 \, \text{g} \)[/tex].
3. Calculate the mass of one pebble:
- We have 124 pebbles that weigh 1,000 grams.
- To find the mass of a single pebble, we divide the total mass by the number of pebbles.
- Mass of one pebble [tex]\[\text{(in grams)} = \frac{1,000 \, \text{grams}}{124 \, \text{pebbles}} \approx 8.065 \, \text{grams} \][/tex].
4. Calculate the number of pebbles in 45,284 grams:
- Now, we need to find out how many pebbles are there in 45,284 grams.
- We use the mass of one pebble calculated in the previous step.
- Number of pebbles = [tex]\[\frac{45,284 \, \text{grams}}{8.065 \, \text{grams/pebble}} \approx 5615.216 \, \text{pebbles} \][/tex].
5. Round to a reasonable number of significant figures:
- The number of pebbles is approximately 5615.216.
- Since we cannot have a fraction of a pebble, we can round this to the nearest whole number.
- Therefore, there are approximately [tex]\( 5615 \)[/tex] pebbles in 45,284 grams.
Thus, in 45,284 grams, there are approximately 5615 pebbles.
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