Question

The product of two decimals is 42.987. If one of them is 12.46, find the other.

Answer 1

Hint: Here we will assume the other number to be x and then multiply it with the given number and then put it equal to the given product.

Complete step by step solution:
Here we are given that:
Product of two decimal numbers is 42.987
Let the numbers be x and y
Then the product can be written as:
\[x \times y = 42.987\]
But the value of x is given to be 12.46
Therefore we have to find the value of y.
Hence,
The above given data can be written as:
\[12.46 \times y = 42.987\]
Now , dividing both the sides by 12.46 we get:
\[
  \dfrac{{12.46 \times y}}{{12.46}} = \dfrac{{42.987}}{{12.46}} \\
  y = \dfrac{{42.987}}{{12.46}} \\
 \]
Now removing the decimal we get:
\[y = \dfrac{{42987}}{{12460}}\]
Solving it further we get:
\[
  y = \dfrac{{345}}{{100}} \\
  y = 3.45 \\ \]
Hence the other number is 3.45

Note:
The multiplication of two numbers is always commutative i.e,
\[x\times y=y\times x\]
Also, If the decimal point is shifted to the right then the power of 10 gets a negative sign with the number of decimal places shifted.
If the decimal point is shifted to the left then the power of 10 gets a positive sign with the number of decimal places shifted.