Question

1. find the remainder when 7,000,000,000,002 is divided by 9.

(a) 0
(b) 1
(c) 2
(d) 8

Explanation:

Identify the given values and target

We need to find the remainder when the large number \(7,000,000,000,002\) is divided by \(9\).

Recall the divisibility rule for 9

A key mathematical rule states that a number is divisible by \(9\) if and only if the sum of its digits is divisible by \(9\). More generally, any integer leaves the same remainder when divided by \(9\) as the sum of its digits does.

Calculate the sum of the digits

Let's sum the individual digits of the number \(7,000,000,000,002\):

$$ \text{Sum} = 7 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 2 $$

$$ \text{Sum} = 7 + 2 = 9 $$

Find the remainder of the sum divided by 9

Now, we divide this sum by \(9\) to find the remainder:

$$ 9 \div 9 = 1 \text{ with a remainder of } 0 $$

Since the sum of the digits is exactly \(9\), which is perfectly divisible by \(9\), the remainder is \(0\).

Answer:

• (A) 0 (Correct answer)
• (B) 1
• (C) 2
• (D) 8