Question

Find \[2\times \dfrac{22}{7}\times 0.35\left( 0.35+1.25 \right)\]. Write the first number after decimal.

Answer 1

Hint: Use the rule of BODMAS and first operate what is asked in brackets then multiplying one by one with each other and then dividing with 7 to get final results.

Complete step-by-step solution -
In the question we have been given the expression \[2\times \dfrac{22}{7}\times 0.35\left( 0.35+1.25 \right)\] and thus we have to find the first digit of decimal.
Now, let’s first write the expression and consider it as P so,
\[\text{P}\ =\ 2\times \dfrac{22}{7}\times 0.35\left( 0.35+1.25 \right)\]
Further calculation we will use the BODMAS for the simplification which means we will first operate the bracket portion.
In the bracket portion it contains the sum of the 0.35 and 1.25 so we will first do the sum first. The sum of 0.35 and 1.25 is 1.60.
Now, the expression holds on as this,
\[\text{P}\ =\ 2\times \dfrac{22}{7}\times 0.35\times 1.60\]
Now, we will multiply one by one so by letting anything unchanged we will multiply 0.35 by 1.60 which is equal to 0.56.
Hence, after multiplication the expression of P becomes,
 \[\text{P}\ =\ 2\times \dfrac{22}{7}\times 0.56\]
Now, we will multiply 0.56 with 2 so, we get \[0.56\times 2\] which is equal to 1.12 so the expression pf P stands as:
\[\text{P}\ =\ \dfrac{22}{7}\times 1.12\]
Now, instead of multiplying 1.12 with 22 we will divide 1.12 by 7 so we get 0.16 and hence the expression of P is:
\[\text{P}\ =\ 22\times 0.16\]
Now, we will find the final product of 22 and 0.16 which is 3.52. So, the given expression who we indicated as P, after calculation we get its value 3.52
So, the number after decimal is 5.
Hence, the answer is 5.

Note: One can also do most of the calculation mentally, firstly adding 0.35 and 1.25 to have 1.60. Then first dividing 0.35 by 7 to get 0.05, then multiplying 0.05 by 2 to 0.1. Now, multiplying 22 by 0.1 we get 2.2 and hence multiplying 2.2 by 1.6 we get 3.52.