Algebra I

Scientific Notation

Lesson

Scientific notation is a compact way to write very large or very small numbers. Every number gets written in the form:

a \times 10^n

where $a$ is a number with absolute value between 1 and 10 (including 1 but not 10), and $n$ is a whole number (positive, negative, or zero).

For large numbers, $n$ is positive: count how many places you move the decimal left to land between 1 and 10.
For small numbers (less than 1), $n$ is negative: count how many places you move the decimal right.

Worked example 1

Convert 4,500 to scientific notation.

Move the decimal 3 places left to land at 4.5:

4{,}500 = 4.5 \times 10^3

Worked example 2

Convert 0.000 27 to scientific notation.

Move the decimal 4 places right to land at 2.7. Because the original number was less than 1, the exponent is negative:

0.00027 = 2.7 \times 10^{-4}

How to type your answer

Use a * for the multiplication and ^ for the exponent. Examples: 4.5*10^3, 2.7*10^-4, 6*10^8.

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

100

Problem 2

1{,}000

Problem 3

0.1

Problem 4

0.01

Practice

Standard problems matching the lesson.

Problem 5

A small city has 4,500 residents. Write in scientific notation.

Problem 6

A stadium seats 32,000. Write in scientific notation.

Problem 7

A region has 750,000 inhabitants. Write in scientific notation.

Problem 8

A nation reports 6,000,000 active users. Write in scientific notation.

Problem 9

A meeting has 120 attendees. Write in scientific notation.

Problem 10

An object measures 0.0027 m wide. Write in scientific notation.

Problem 11

A particle weighs 0.00045 g. Write in scientific notation.

Problem 12

A bacterium is 0.0001 mm wide. Write in scientific notation.

Problem 13

An acid concentration is 0.082 mol/L. Write in scientific notation.

Problem 14

Global population reaches 9,000,000,000. Write in scientific notation.

Problem 15

A wavelength is 0.0000056 m. Write in scientific notation.

Problem 16

A library has 12,500 books. Write in scientific notation.

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 17

A company reports 875,000,000 dollars in revenue. Write in scientific notation.

Problem 18

A virus measures 0.000000091 m. Write in scientific notation.

Problem 19

A school has 6,750 students. Write in scientific notation.

Problem 20

A chemical is at 0.000156 mol/L. Write in scientific notation.

Problem 21

A planet's mass is 23,000,000 kg (scaled). Write in scientific notation.

Problem 22

A tiny distance: 0.00000000034 m. Write in scientific notation.

Practice

Standard problems matching the lesson.

Problem 23

The distance from Earth to the Sun is about 93,000,000 miles. Write in scientific notation.

Problem 24

A virus is about 0.000000125 m long. Write in scientific notation.

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 25

Light travels about 300,000,000 meters per second. Write in scientific notation.

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