Question

Evaluate the following by using the identities:
$9.7\times 9.8$.

Answer 1

Given that, $9.7\times 9.8$.

The given expression can be written as ,

$9.7\times 9.8$ $=(10-0.2)(10-0.3)$.

We know, $(x+a)(x+b)=x^2+(a+b)x+ab$.

Then, we get ,

$9.7\times 9.8$ $=(10-0.2)(10-0.3)$

$=(10{)}^2+(-0.2-0.3)10+(-0.2\left)\right(-0.3)$

$=100+(-0.5)10+0.06$

$=100-5+0.06$

$=95+0.06$

$=95.06$.

Hence, the required answer is $95.06$.