Scientific notation: from a virus to the Sun
Write the sizes of a virus, a hair, Mount Everest and the distance to the Sun in standard form, a × 10ⁿ, on a powers-of-ten ruler.
Core concept
Any positive number can be written as a × 10ⁿ with 1 ≤ a < 10; n counts how many places the decimal point moves
Topic: Scientific notation
Mount Everest is about 8,800 m high; a virus is about 0.0000001 m across; the Sun is about 150,000,000,000 m away. Long rows of zeros are hard to read and easy to miscount, so scientists write such numbers in standard form: a × 10ⁿ, where a is at least 1 and less than 10. Everest is 8.8 × 10³ m because the decimal: A number with a point, like 2.5, where the digits after the point are tenths, hundredths … All key words point of 8.8 moves 3 places to the right to make 8,800. Small numbers have negative powers: the virus is 1 × 10⁻⁷ m, because the point moves 7 places to the left.
What you will learn
- Write large and small numbers in standard form a × 10ⁿ.
- Convert from standard form back to ordinary numbers.
- Compare sizes using powers of ten.
Before you start
- Powers of ten and negative indices.
Materials
- A list of sizes from a science book
Equipment
- A ruler marked in mm
Procedure
- Tap the chip to choose an object to measure.
- Tap − or + to set a and the power n so that a × 10ⁿ matches the object's size.
- Read the number written out in full, and watch the pointer on the ruler.
- Match Mount Everest, a virus, the distance to the Sun and the width of a hair, and record each.
How this simulation is simplified
- Sizes are rounded to two significant figures.