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Answer :
The sum of the weight of the empty box and the 940 feathers is approximately [tex]5.90 \times {10}^{ - 1} [/tex] kg.
What is a scientific notation?
A number is expressed using scientific notation when it contains a number larger than 1 but less than 10, that multiplies a power of 10
The empty weight of the box = 56.7 grams
The number of feathers added = 940 feathers
Mass of one feather (unit weight) = 0.000567 kilogram
The total weight of the box with the 940 feathers is found as follows;
56.7 grams = 0.0567 kilograms
Mass of the empty box in kilograms = 0.0567 kilograms
Total mass of the 940 feathers 0.000567 × 940 = 0.53298 kilograms
The total weight of the box with the 940 feathers inside is; 0.0567 kilograms + 0.53298 kilograms = 0.58968 kilograms
The total weight of the box and the feathers = 0.58968 kilograms =
[tex]5.8968 \times {10}^{ - 1} [/tex]
kilograms
Rounding the coefficient to the nearest tenth gives;
The total weight of the box and the feathers is approximately [tex]5.90 \times {10}^{ - 1} [/tex] kilograms
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The total weight of the box with 940 feathers is calculated by adding the weight of the empty box (converted to kilograms) to the total weight of the feathers, which results in 0.59028 kg. This is then expressed in scientific notation as 5.9 × 10⁻¹ kg, rounded to the nearest tenth.
The weight of an empty box is 56.7 grams. To find the total weight of the box with 940 feathers inside, we first calculate the total weight of the feathers in kilograms. Since each feather weighs 0.000567 kilogram, we multiply this weight by the number of feathers:
Total weight of feathers = 0.000567 kg/feather × 940 feathers = 0.53358 kg
We then add the weight of the empty box, which we must convert from grams to kilograms. The weight of the box is 56.7 grams, and since there are 1000 grams in a kilogram:
Weight of the empty box in kilograms = 56.7 grams × (1 kg/1000 grams) = 0.0567 kg
Now, we can find the total weight:
Total weight of the box with feathers = Weight of the empty box + Total weight of feathers = 0.0567 kg + 0.53358 kg = 0.59028 kg
To express this answer in scientific notation, rounded to the nearest tenth as the least-precise measurement is to the 0.1 decimal place:
Total weight in scientific notation = 5.9 × 10⁻¹ kg
