Scientific Notation Examples: 45 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Scientific Notation.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

A way of writing very large or very small numbers as $a \times 10^n$ , where $1 \leq |a| < 10$ and $n$ is an integer.

Instead of writing out all the zeros in 93,000,000 or 0.000042, you slide the decimal point and count how many places it moved. The exponent on 10 keeps track of the shift.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Scientific notation separates a number into a size between 1 and 10 and a power of ten.

Common stuck point: The procedure for scientific notation is the easy part; the trap is choosing a first factor outside $1\le a<10$ . Asking "Is the first factor at least 1 and less than 10?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Is the first factor at least 1 and less than 10?

Worked Examples

Example 1

easy

Write

0.00047

in scientific notation.

Answer

4.7 \times 10^{- 4}

First step

Move the decimal point right until we have a number between 1 and 10:

4.7

Full solution

2
Count the places moved: 4 places to the right, so the exponent is $-4$ .
3
Result: $4.7 \times 10^{-4}$ .

Scientific notation expresses a number as

a \times 10^n

where

1 \leq a < 10

. Moving the decimal right gives a negative exponent; moving it left gives a positive exponent.

Example 2

medium

Compute

(3.0 \times 10^5) \times (2.0 \times 10^{-3})

and express the answer in scientific notation.

Example 3

easy

Write 1 million in scientific notation.

Example 4

medium

A virus is

1.2 \times 10^{-7}

m wide. Express this in standard form.

Example 5

hard

Earth's mass is about

6 \times 10^{24}

kg, Moon's mass is about

7.3 \times 10^{22}

kg. How many times more massive is Earth than the Moon?

Example 6

hard

Compute

(2 \times 10^{-4})^3

in scientific notation.

Example 7

challenge

The mass of one atom of carbon is about

1.99 \times 10^{-23}

12\times10^4

in proper scientific notation? If not, fix it.

Example 8

easy

Write

400

in scientific notation.

Example 9

easy

Convert

6.5\times10^0

to standard form.

Example 10

easy

Which is larger:

3\times10^5

9\times10^4

Example 11

medium

Multiply

(2\times10^3)(4\times10^5)

Example 12

medium

Divide

\frac{8\times10^6}{2\times10^2}

Example 13

medium

Multiply

(5\times10^3)(6\times10^4)

and put the result in proper form.

Example 14

medium

Add

3\times10^4+5\times10^4

Example 15

medium

Add

4\times10^5+3\times10^4

Example 16

medium

The mass of a proton is about

1.6\times10^{-27}

kg. Write this in standard form.

Example 17

medium

Express

0.00056\times10^3

in proper scientific notation.

Example 18

challenge

Light travels

3\times10^8

m/s. How far in

2\times10^2

seconds? Give scientific notation.

Example 19

challenge

Estimate how many times larger

6\times10^{12}

is than

3\times10^4

Example 20

challenge

Simplify

\frac{(4\times10^5)(3\times10^{-2})}{6\times10^1}

in scientific notation.

Example 21

medium

Write

0.0036\times10^5

in proper scientific notation.

Example 22

medium

Square

(3\times10^4)^2

and give scientific notation.

Example 23

easy

Write

250{,}000

in scientific notation.

Example 24

easy

Write

0.00038

in scientific notation.

hard

Express

0.000506

in scientific notation with proper form.

Example 36

hard

A computer performs

5 \times 10^9

operations per second. How many operations does it do in

2 \times 10^3

seconds?

Example 37

hard

Compute

\sqrt{9 \times 10^{16}}

in scientific notation.

Example 38

challenge

A bacterial culture starts with

2 \times 10^4

cells and doubles every hour. How many cells after 10 hours? Express in scientific notation.

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Related Concepts

Exponent Rules Place Value Decimals Scientific Notation Operations Significant Figures

Background Knowledge

These ideas may be useful before you work through the harder examples.

exponent rulesplace valuedecimals