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.

Work through these. Stuck? Click Get a hint.

Quick problems to get going.

Problem 1

100

Problem 2

1{,}000

Problem 3

0.1

Problem 4

0.01

Standard problems matching the lesson.

Problem 5

4{,}500

Problem 6

32{,}000

Problem 7

750{,}000

Problem 8

6{,}000{,}000

Problem 9

120

Problem 10

0.0027

Problem 11

0.00045

Problem 12

0.0001

Problem 13

0.082

Problem 14

9{,}000{,}000{,}000

Problem 15

0.0000056

Problem 16

12{,}500

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

Problem 17

875{,}000{,}000

Problem 18

0.000000091

Problem 19

6{,}750

Problem 20

0.000156

Problem 21

23{,}000{,}000

Problem 22

0.00000000034