Question

Find the value of $1.3 \times 3.1$

Answer 1

Hint: The given problem is of multiplication involving decimal numbers. We can solve this by converting into fraction or by direct multiplication. We know that 0.1 can be written in fraction as \[\dfrac{1}{{10}}\], similarly 0.01 can be written in fraction as \[\dfrac{1}{{100}}\] and so on. Using this method of converting we can solve the above multiplication easily.

Complete step-by-step solution:
The given expression is $1.3 \times 3.1$
We know that 1.3 can be written as \[1\dfrac{3}{{10}}\]. (Because we have 0.3)
Similarly 3.1 can be written as \[3\dfrac{1}{{10}}\]. (Because we have 0.1)
Now multiplying these two,
\[ \Rightarrow = 1\dfrac{3}{{10}} \times 3\dfrac{1}{{10}}\]
Since they are in mixed fraction we convert it into improper fraction.
\[ \Rightarrow = \dfrac{{10 + 3}}{{10}} \times \dfrac{{30 + 1}}{{10}}\]
\[ \Rightarrow = \dfrac{{13}}{{10}} \times \dfrac{{31}}{{10}}\]
Using simple multiplication, we have
\[ \Rightarrow = \dfrac{{403}}{{100}}\]
Since in the denominator we have 100 we put a decimal point at 2nd place counting from right to left. That is,
\[ \Rightarrow = 4.03\]
Hence, the value of multiplication of two numbers $1.3 \times 3.1 = 4.03$
(Using the observation, we can suggest that the sum of the number of decimal places in the factors equal to the number of decimal places in the product. That is 1.3 we have 1 decimal place, in 3.1 we have one decimal place while in the product we have two decimal places.)

Note: If we follow the direct multiplication. Care must be taken while adding numbers which have sum more than 9 and the carry which has to be placed on the next number. Remember while taking decimal as fraction in above it will be in mixed fraction. We don’t multiply it directly, we convert the mixed fraction into an improper fraction then we multiply.