Question

Solve \[100x\left( {0.01x - 0.1942} \right)\].

Answer 1

Hint: We will first simplify the given expression and then multiply by 100 x to get the desired expression.
When a decimal number is multiplied by \[{10^a}\] where ‘a’ is positive then the decimal point gets shifted to ‘a’ places the right of the decimal number.

Complete step-by-step answer:
The given expression is:-
\[100x\left( {0.01x - 0.1942} \right)\]
Multiplying 100 inside the bracket we get:
\[100x \times 0.01x - 100x \times 0.1942\]
Now we know that when a decimal number is multiplied by \[{10^a}\] where ‘a’ is positive then the decimal point gets shifted to ‘a’ places the right of the decimal number.
Since, here we are multiplying the decimal numbers by 100x i.e.\[{10^2}\]x
Hence, the decimal place will get shifted to right by 2 places.
Therefore simplifying the above expression we get:-
\[1 \times x \times x - x \times 19.42\]
Simplifying it further we get:-
\[ \Rightarrow {x^2} - 19.42x\]

Hence, \[{x^2} - 19.42x\] is the required answer.

Additional Information:
When a number is multiplied by \[{10^a}\] where ‘a’ is negative then the decimal point is shifted to the left by ‘a’ places.
For a whole number eg – 10
We can write it as \[10.0\] and then apply the rules.

Note: Students can also convert the decimals into fractions first by dividing the number by \[{10^a}\] such that ‘a’ is the number of digits after the decimal point.
Hence, the given expression can be written as:
\[100x\left( {\dfrac{1}{{100}}x - \dfrac{{1942}}{{10000}}} \right)\]
Now multiplying by 100x we get:-
\[100x \times \dfrac{1}{{100}}x - 100x \times \dfrac{{1942}}{{10000}}\]
Simplifying it further we get:-
\[1 \times x \times x - x \times 19.42\]
\[ \Rightarrow {x^2} - 19.42x\]