What is a googol multiplied by 100? How many zeros will it have?
The correct answer and explanation is:
A googol is a number that is written as 1 followed by 100 zeros. When you multiply a googol by 100, you’re essentially adding two more zeros to the number. Therefore, a googol multiplied by 100 would be written as: 10000000000⋯000⏟100 zeros×100=10000000000⋯0000000⏟102 zeros1 \underbrace{0000000000 \cdots 000}_{100 \text{ zeros}} \times 100 = 1 \underbrace{0000000000 \cdots 0000000}_{102 \text{ zeros}}
So the result is a 1 followed by 102 zeros.
Explanation:
To understand this, let’s break it down:
- A googol is a very large number that is equal to 1010010^{100}, which means 1 followed by 100 zeros.
- When multiplying a number by 100, you are effectively multiplying it by 10210^2 (since 100 is 10210^2).
- So, multiplying 1010010^{100} by 10210^2 results in 1010210^{102}, which is simply the number 1 followed by 102 zeros.
- This result can also be written as a 1 followed by 102 zeros in standard decimal notation, which represents the large number.
Therefore, the number formed by multiplying a googol by 100 has 102 zeros in total. The multiplication of large numbers like this is a way of demonstrating the sheer magnitude of numbers that extend far beyond what is typically encountered in everyday life.