Vivaan has $45.75 in his checking account. He used his debit card for a $105.80 purchase. How much money does Vivaan have in his checking account?

Vivaan has $45.75 - $105.80 = $<<45.75-105.80=-60.05>>60.05 in his checking account. Answer: \boxed{60.05}.

To find out how much money Vivaan has in his checking account after the $105.80 purchase, you need to subtract $105.80 from $45.75.

Step 1: Subtract the purchase amount from the initial balance:
$45.75 - $105.80 = -$60.05

So, Vivaan has a balance of -$60.05 in his checking account after the $105.80 purchase.