Step 1: See what each fold does

Every time you fold the paper in half, the number of layers doubles.

0 folds: 1 layer
1 fold: 2 layers
2 folds: 4 layers
3 folds: 8 layers

So after n folds, there are 2ⁿ layers.

Step 2: Count the layers after 20 folds

2²⁰ = 1,048,576 layers

A handy shortcut: 2¹⁰ = 1,024, which is about 1,000. So 2²⁰ = 2¹⁰ × 2¹⁰ ≈ 1,000 × 1,000 = about 1 million layers.

Step 3: Multiply by the thickness of one sheet

1,048,576 × 0.2 mm = 209,715.2 mm

Step 4: Convert to meters

There are 1,000 mm in 1 meter:

209,715.2 mm ÷ 1,000 ≈ 210 meters

This is closest to C. About 200 meters.

Fun fact: That's taller than most skyscrapers, from a sheet of paper thinner than a fingernail. This shows how fast doubling grows. In real life, though, most paper can't be folded more than about 7 or 8 times.

Quick Method: Use 2¹⁰ ≈ 1,000

Fast steps

20 folds = 2²⁰ layers.
Split it: 2¹⁰ × 2¹⁰ ≈ 1,000 × 1,000 = about 1 million layers.
0.2 mm × 1 million = 200,000 mm.
200,000 mm = 200 meters → answer C.

Extra trick for converting units

Remember that 1 million millimeters = 1 kilometer (because 1 km = 1,000 m = 1,000,000 mm). So:

0.2 mm × 1 million = 0.2 km = 200 m

No need to write out all those zeros.

Why is estimating safe here?

The exact value is 2²⁰ = 1,048,576, so the true answer is about 210 meters. That's only about 5% off, while the answer choices are far apart (10, 100, 200, 500). Also, the question says "about", which is a signal that an estimate is expected.

Worth memorizing for AMO

Power	Exact value	Estimate
2¹⁰	1,024	≈ 1 thousand
2²⁰	1,048,576	≈ 1 million
2³⁰	about 1.07 billion	≈ 1 billion

Every 10 extra folds multiplies the result by roughly 1,000. So if the question asked for 30 folds, the answer would be about 0.2 mm × 1 billion = 200 km.

AMO Grade 5-6

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