Practice Scientific Notation in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A way of writing very large or very small numbers as a×10n, where 1≤∣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.

Showing a random 20 of 50 problems.

Example 1

medium
Add 4×105+3×104.

Example 2

medium
A virus is 1.2×10−7 m wide. Express this in standard form.

Example 3

challenge
A bacterial culture starts with 2×104 cells and doubles every hour. How many cells after 10 hours? Express in scientific notation.

Example 4

easy
Write 400 in scientific notation.

Example 5

medium
What power of 10 is 1 billion?

Example 6

easy
Is 0.45×106 in proper scientific notation? If not, fix it.

Example 7

medium
Multiply (5×103)(6×104) and put the result in proper form.

Example 8

medium
The mass of a proton is about 1.6×10−27 kg. Write this in standard form.

Example 9

hard
Compute (2.5×106)2 in scientific notation.

Example 10

challenge
Estimate how many times larger 6×1012 is than 3×104.

Example 11

easy
Convert 6.5×100 to standard form.

Example 12

hard
Add 3.0×105+4.0×104 in scientific notation.

Example 13

easy
Convert 8×104 to standard form.

Example 14

hard
Earth's mass is about 6×1024 kg, Moon's mass is about 7.3×1022 kg. How many times more massive is Earth than the Moon?

Example 15

medium
Compute (4×103)(2×105) in scientific notation.

Example 16

easy
Convert 7×10−4 to standard form.

Example 17

easy
Write 0.000042 in scientific notation.

Example 18

hard
Order from least to greatest: 4×10−5,3×10−4,2×10−5.

Example 19

hard
Compute 9×1016 in scientific notation.

Example 20

challenge
Simplify (4×105)(3×10−2)6×101 in scientific notation.
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