Practice Scientific Notation in Math

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

Worksheet PDF Free Answer-key PDF Family

Quick Recap

A way of writing very large or very small numbers as a×10na \times 10^n, where 1≤∣a∣<101 \leq |a| < 10 and nn 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+3×1044\times10^5+3\times10^4.

Example 2

medium
A virus is 1.2×10−71.2 \times 10^{-7} m wide. Express this in standard form.

Example 3

challenge
A bacterial culture starts with 2×1042 \times 10^4 cells and doubles every hour. How many cells after 10 hours? Express in scientific notation.

Example 4

easy
Write 400400 in scientific notation.

Example 5

medium
What power of 10 is 11 billion?

Example 6

easy
Is 0.45×1060.45 \times 10^6 in proper scientific notation? If not, fix it.

Example 7

medium
Multiply (5×103)(6×104)(5\times10^3)(6\times10^4) and put the result in proper form.

Example 8

medium
The mass of a proton is about 1.6×10−271.6\times10^{-27} kg. Write this in standard form.

Example 9

hard
Compute (2.5×106)2(2.5 \times 10^6)^2 in scientific notation.

Example 10

challenge
Estimate how many times larger 6×10126\times10^{12} is than 3×1043\times10^4.

Example 11

easy
Convert 6.5×1006.5\times10^0 to standard form.

Example 12

hard
Add 3.0×105+4.0×1043.0 \times 10^5 + 4.0 \times 10^4 in scientific notation.

Example 13

easy
Convert 8×1048 \times 10^4 to standard form.

Example 14

hard
Earth's mass is about 6×10246 \times 10^{24} kg, Moon's mass is about 7.3×10227.3 \times 10^{22} kg. How many times more massive is Earth than the Moon?

Example 15

medium
Compute (4×103)(2×105)(4 \times 10^3)(2 \times 10^5) in scientific notation.

Example 16

easy
Convert 7×10−47\times10^{-4} to standard form.

Example 17

easy
Write 0.0000420.000042 in scientific notation.

Example 18

hard
Order from least to greatest: 4×10−5,3×10−4,2×10−54 \times 10^{-5}, 3 \times 10^{-4}, 2 \times 10^{-5}.

Example 19

hard
Compute 9×1016\sqrt{9 \times 10^{16}} in scientific notation.

Example 20

challenge
Simplify (4×105)(3×10−2)6×101\frac{(4\times10^5)(3\times10^{-2})}{6\times10^1} in scientific notation.
← Back to Scientific Notation Worked Examples Formula Explained