Question

A bag contains 100 \[A\times 4\] sheets. The weight of an \[A\times 4\] sheet is 0.01 mg and the weight of an empty bag is 6.00 g. Find the weight of the bag alone with all \[A\times 4\] sheets.

Answer 1

Hint: In this question, we first need to convert the given weight of each \[A\times 4\] sheet in mg to g. Then find the weight of all the 100 \[A\times 4\] sheets by multiplying the weight of each sheet with 100. Now, add the weight of the bag to this weight of all the sheets to get the total weight.

Complete step by step solution:
Now, given in the question that there are 100 \[A\times 4\] sheets in the bag
Here, given that the weight of each sheet is 0.01 mg
As we already know the conversion between the grams and milligrams we have
\[1g=1000mg\]
Now, the weight of each \[A\times 4\]sheet is given by
\[\Rightarrow \dfrac{0.01}{1000}g\]
Now, on further simplifying it we get,
\[\Rightarrow {{10}^{-5}}g\]
Now, let us find the weight of 100 \[A\times 4\] . We have the weight of single unit and also the number of units, so we can multiply 100 with weight of each sheet
\[\Rightarrow {{10}^{-5}}\times 100g\]
Now, on simplifying this further we get,
\[\Rightarrow 0.001g\]
Now, to get the weight of bag alone with all the \[A\times 4\] sheets we need to add the weight of 100 \[A\times 4\] sheets to the weight of the bag
Here, given that the weight of the bag is 6.00 gm
Now, the weight of the bag with all \[A\times 4\] sheets is given by,
\[\Rightarrow 6.00+0.001g\]
Now, this can be further written in the simplified form as
\[\Rightarrow 6.001g\]
Hence, the weight of the bag alone with all the \[A\times 4\] sheets is 6.001 gm

Note: Instead of converting the weight of each bag from milligrams to grams we can also solve it by first finding the weight of all the 100 sheets in milligrams and then converting it to grams to add it to the weight of the bag. Both the methods give the same result.
It is important to note that we need to convert either the weight of the sheets to grams or the weight of the bag to milligrams. Because if we add both of them without converting them to the same unit then we get the incorrect result.