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Have a go at this without a calculator....
26 Answers
Imagine that you can fold a piece of paper as many times as you want to (we all know it's about 8 times in reality).
This piece of paper is one thousandth of an inch thick (0.001")
You are to fold this piece of paper exactly in half for 50 times.
What is the total thickness from top to bottom of this piece of folded paper?
This piece of paper is one thousandth of an inch thick (0.001")
You are to fold this piece of paper exactly in half for 50 times.
What is the total thickness from top to bottom of this piece of folded paper?
Answers
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I'd work it out like this:
2^10 = 1000 (roughly)
so 2^50 = 1000^5
If the paper was 0.001 mm thick (I have to think in metric) one factor of 1000 would make it 1 mm. Two more factors of 1000 would make it 1 km. We are left with two factors of 1000. So the answer would be 1 million kilometres.
An inch is 25.4mm, increasing the answer to 25.4 million kilometres.
The approximation 2^10 = 1000 is 2.4% too small, so we need to increase the answer by 2.4% five times. This will be a bit more than 12% as it is compounded. Let's guess 12.5% becaue that is one-eighth i.e. about 3.2 million kilometres.
Answer = 25.4 + 3.2 = 28.6 million kilometres.
How did I do?
2^10 = 1000 (roughly)
so 2^50 = 1000^5
If the paper was 0.001 mm thick (I have to think in metric) one factor of 1000 would make it 1 mm. Two more factors of 1000 would make it 1 km. We are left with two factors of 1000. So the answer would be 1 million kilometres.
An inch is 25.4mm, increasing the answer to 25.4 million kilometres.
The approximation 2^10 = 1000 is 2.4% too small, so we need to increase the answer by 2.4% five times. This will be a bit more than 12% as it is compounded. Let's guess 12.5% becaue that is one-eighth i.e. about 3.2 million kilometres.
Answer = 25.4 + 3.2 = 28.6 million kilometres.
How did I do?