Question

Solve the following equation.
\[10.05\times 1.05\]

Answer 1

Hint: For doing the multiplication, we will first write 10.05 as (10 + 0.05) and 1.05 as (1 + 0.05). So, we can write \[10.05\times 1.05\text{ as }\left( 10+0.05 \right)\times \left( 1+0.05 \right)\] and hence evaluate it to get the result using the formula (a + b) (c + d) = ac + ad + bc + bd.

Complete step-by-step solution -
In the question, we are given two numbers 10.05 and 1.05 and we have to multiply it with each other to evaluate it. Now, before proceeding, let’s learn about multiplication. Multiplication (often denoted by the cross symbol \[\times \] or a dot operator “.” or by an asterisk “*”) is one of the four elementary operators of arithmetic, while the others being addition, subtraction, and division. The result of a multiplication is called the product.
The multiplication of whole numbers is often referred to as repeated addition, which is the multiplication of two numbers equivalent to adding as many as copies. So, we are given \[10.05\times 1.05.\]
We can write \[10.05\text{ as }\left( 10+0.05 \right)\text{ and }1.05\text{ as }\left( 1+0.05 \right)\]
So, we can write \[10.05\times 1.05\text{ as }\left( 10+0.05 \right)\times \left( 1+0.05 \right)\]
Now, we can evaluate using the formula (a + b) (c + d) = ac + ad + bc + bd.
So, \[10.05\times 1.05\] can be evaluated as
\[\left( 10+0.05 \right)\left( 1+0.05 \right)\]
\[\Rightarrow 10+10\times 0.05+1\times 0.05+0.05\times 0.05\]
\[\Rightarrow 10+0.5+0.05+0.0025\]
So, on adding together, we get 10.5525.
Hence, the value of \[10.05\times 1.05\] is 10.5525.

Note: We can also do the same question by another method. We can write the given decimals or fractions like 10.05 as \[\dfrac{1005}{100}\] and 1.05 as \[\dfrac{105}{100}.\] Here, we can write \[10.05\times 1.05\] as \[\dfrac{1005}{100}\times \dfrac{105}{100}\] and hence evaluate.