Question

How do you simplify \[\left( {0.15} \right)\left( {3.2} \right)\]?

Answer 1

Hint: Here we have to multiply two decimal numbers. Multiplication of decimal numbers is similar to integers with one change that we have to include the decimal point in the final result. Decimal numbers can be multiplied first without decimal points and then placing the decimal point appropriately in the result

Complete step-by-step solution:
We have to simplify the expression \[\left( {0.15} \right)\left( {3.2} \right)\].
Here two decimal numbers are given in brackets side-by-side without any mathematical operator sign in between so we have to multiply the numbers.
\[\left( {0.15} \right)\left( {3.2} \right) = 0.15 \times 3.2\]
The first number is $0.15$ which has two digits after the decimal point.
And the second number is $3.2$ which has one digit after the decimal point.
A simple way to multiply the decimal numbers is to first multiply them without decimal points and then place the decimal point at the appropriate place in the result.
So, $0.15$ becomes $15$ and $3.2$ becomes $32$ without decimal points.
We multiply $15$ and $32$,
$15 \times 32 = 480$
In the result that we get after multiplication without decimal point, we now have to place the decimal point appropriately.
In the given decimal numbers $0.15$ has decimal point before $2$ digits and $3.2$ has decimal point before $1$ digit.
So we have to place the decimal point before $2 + 1 = 3$ digits in $480$.
We get, $0.480 = 0.48$
Hence, the result of multiplying $0.15$ and $3.2$ is $0.48$.
Additional Information: Decimal numbers can also be represented as fractions. After operating on fractions the result can be represented as decimal number to arrive at the solution.


Note: While converting a decimal number into a fraction, we calculate the number of digits after the decimal point and we multiply the numerator and the denominator with \[1\] with that many zeros in it. For example, for the decimal number $0.85$to be converted into a fraction, the numerator $0.85$ and the denominator $1$ will be multiplied with $100$. The formula of ${(a + b)^2} = {a^2} + {b^2} + 2ab$ should be carefully used when the terms are in fractions or when there are variables in fractions.