Question

The number of zeros occurring after the last
significant (non zero) digit in the product of
75 x 60 x 48 x 35 x 30 x 24x 18 x 10 x 5 is
1.5 2.6
4.9​

Answer 1

Step-by-step explanation:

is equal to 4.8..................... which is equal to 4.9.

..............

Answer 2

Concept

The number of zero is equal to the common factor of $2^n$ and $5^n$

The number of zero = n

Given

The product of 75 x 60 x 48 x 35 x 30 x 24x 18 x 10 x 5

Find

The number of zeros occurring after the last significant (non zero) digit in the product

Solution

By using factorization method, we find the factors of the numbers.

$Factor\ of\ 75 = 1 * 3 * 5^2\\The\ factor\ of\ 60 = 1 * 2^2 * 3 * 5\\The\ factor\ of\ 48 = 1 * 2^4 * 3\\The\ factor\ of\ 35= 1 * 5 * 7\\The\ factor\ of\ 30 = 1 * 2 * 3 * 5\\The\ factor\ of\ 24 = 1 * 2^3 *3\\The\ factor\ of\ 18 = 1 * 2 * 3^2\\The\ factor\ of\ 10 = 1*2*5\\The\ factor\ of\ 5 = 1*5$

Now, we know that, the number of zero is equal to the common factor of $2^n$ and $5^n$.

Total Factors of 2 = $2^{12}$

Total factors of 5 = $5^7$

Common fators of 2 and 5 = $2^7 * 5^7$

Thus, $n = 7$

Therefore, The number of zeros occurring after the last significant (non zero) digit in the product is 7