Scientific Notation

The average distance from the Earth to the Sun, 149,600,000 km, can be written in shorthand notation as…

1.496 × 10⁸ km

The diameter of the hydrogen atom, 0.000,000,000,11 m, can be written in shorthand notation as…

1.1 × 10^–10 m

The mass of the electron, 0.000,000,000,091 kg, can be written in shorthand notation as…

9.1 × 10^–11 kg

The mean distance of Saturn from the Sun, 1,427,000,000 km, can be written in shorthand notation as…

1.427 × 10⁹ km

There are 1000 mm in 1 meter. This means that a distance of 10mm is…

1 × 10^–2 m

0.034 meter is what?

34 mm

10² × 10⁵ =

10,000,000

10⁰ (10 to the power 0)

1

The number 50,000 is written in powers-of-ten notation as…

5 × 10⁴

10^–3 × 10³ =

1

(3 × 10⁴)⁴ =

8.1 × 10¹⁷

(1/2)⁴ =

6.25 × 10^–2

(0.5)³ =

0.125

10⁴ × 10⁸ =

10¹²

10⁸/10⁹ =

10^-1

(8.0 × 10⁵)/(2 × 10³⁾ =

400

10⁵/10⁵ =

1

1.5 × 10⁴ × 1.5 × 10^–4 =

1.25

One billionth divided by one millionth is equal to…

10^-3

(2 × 10³)³ =

8 × 10⁹

By what approximate factor, in powers-of-ten notation, is a human being (height about 2 m) larger than the nucleus of a hydrogen atom, or proton (diameter about 10^–15 m)?

2 × 10¹⁵

By how many powers of ten is the diameter of the Sun (1.4 × 10⁵ km) greater than the length of a beetle (14 mm)?

10

In this age of space exploration, man has now traveled to the Moon. By how many orders of magnitude (powers of ten) was this journey greater than that of Columbus when he traveled from the Old World to the Americas?

2 orders of magnitude

If there are about 6000 stars in the entire sky that can be seen by the unaided human eye, about how many stars would be seen at a particular instant on a given dark night from a single location with an uninterrupted distant horizon?

3,000