Table of Contents

Welcome to our **scientific notation calculator**!

Actually, our app is a scientific notation **conversion calculator** because it can do both, convert and calculate.

## Calculator

## How the Calculator Works

When you come to this page, then the calculator is shown in expanded form so that you can carry out the mathematical operation you want.

Fill in the first value, then click the corresponding operation symbol:

Our scientific notation calculations include adding, subtracting, dividing as well as multiplying scientific notation.

Next fill in the second value.

There is no result button, because the outcome is computed automatically once all required input forms have been filled.

Note that you can optionally switch to e **notation** as well as to **decimal notation** – the numbers and the result always follow.

It essentially means that our app is also a decimal to scientific notation **converter**, and vice versa.

In this case you may want to press *collapse* first.

Needless to say that you can expand our online tool (again) after that.

BTW: If you are looking for a scientific calculator, we recommend the one you find on google.com.

## Scientific Notation Terms

For m × 10^{n} we employ the following terms:

**Coefficient**: m, also called significand and mantissa**Base**: 10**Index**: n, also called exponent**Normalized**notation: 1 ≤ |m| < 10**Significant figure**: A digit in the coefficient that adds to its precision.

### Scientific Notation Calculator Multiplication

Scientific notation multiplication uses the multiplying exponents rule known from exponentiation.

a × 10^{n} × b × 10^{m} = (a × b) × 10^{n+m}

Example:

4 × 10^{2} × 2 × 10^{3} = 8 × 10^{5}

### Scientific Notation Calculator Division

Scientific notation division uses the dividing exponents rule also known from exponentiation.

a × 10^{n} / b × 10^{m} = a/b × 10^{n-m}

Example:

4 × 10^{4} / 2 × 10^{2} = 2 × 10^{2}

### Scientific Notation Calculator Addition

Scientific notation additions requires the same exponents for both summands; thus that the significands can be simply added:

a × 10^{n} + b × 10^{n} = (a + b) × 10^{n}

Example:

1.5 × 10^{3} + 3.25 × 10^{3} = 4.75 × 10^{3}

### Scientific Notation Calculator Subtraction

Scientific notation subtraction requires the same exponents for both terms; thus that the significands can be simply subtracted:

a × 10^{n} – b × 10^{n} = (a – b) × 10^{n}

Example:

4 × 10^{6} – 2 × 10^{6} = 2 × 10^{6}

Our exponential notation calculator can be found here.

We also have students practice: scientific notation practice. Or would you rather take our quiz with questions in the context of this site?

In the next part you can find our compilation of frequent decimal form to scientific form conversions.

## Frequent Scientific Notation Examples

The following table contains frequent conversions from standard form to scientific:

Decimal Value | Scientific Notation |
---|---|

0.00002 | 2 × 10^{-5} |

0.00003 | 3 × 10^{-5} |

0.00005 | 5 × 10^{-5} |

0.0001 | 1 × 10^{-4} |

0.0003 | 3 × 10^{-4} |

0.00038 | 3.8 × 10^{-4} |

0.0005 | 5 × 10^{-4} |

0.00063 | 6.3 × 10^{-4} |

0.0008 | 8 × 10^{-4} |

0.001 | 1 × 10^{-3} |

0.00125 | 1.25 × 10^{-3} |

0.0023 | 2.3 × 10^{-3} |

0.0024 | 2.4 × 10^{-3} |

0.0026 | 2.6 × 10^{-3} |

0.0042 | 4.2 × 10^{-3} |

0.0045 | 4.5 × 10^{-3} |

0.0048 | 4.8 × 10^{-3} |

0.005 | 5 × 10^{-3} |

0.0053 | 5.3 × 10^{-3} |

0.008 | 8 × 10^{-3} |

0.0082 | 8.2 × 10^{-3} |

0.0096 | 9.6 × 10^{-3} |

0.03054 | 3.054 × 10^{-2} |

0.12 | 1.2 × 10^{-1} |

1 | 1 × 10^{0} |

1.024 | 1.024 × 10^{0} |

2 | 2 × 10^{0} |

2.5 | 2.5 × 10^{0} |

3 | 3 × 10^{0} |

3.3 | 3.3 × 10^{0} |

4 | 4 × 10^{0} |

4.8 | 4.8 × 10^{0} |

5 | 5 × 10^{0} |

5.75 | 5.75 × 10^{0} |

6 | 6 × 10^{0} |

6.0012 | 6.0012 × 10^{0} |

6.023 | 6.023 × 10^{0} |

6.7 | 6.7 × 10^{0} |

7 | 7 × 10^{0} |

7.0042 | 7.0042 × 10^{0} |

7.85 | 7.85 × 10^{0} |

8 | 8 × 10^{0} |

9 | 9 × 10^{0} |

9.03 | 9.03 × 10^{0} |

10 | 1 × 10^{1} |

12 | 1.2 × 10^{1} |

19 | 1.9 × 10^{1} |

24 | 2.4 × 10^{1} |

31 | 3.1 × 10^{1} |

34.216 | 3.4216 × 10^{1} |

45 | 4.5 × 10^{1} |

45.01 | 4.501 × 10^{1} |

52 | 5.2 × 10^{1} |

60 | 6 × 10^{1} |

78 | 7.8 × 10^{1} |

84 | 8.4 × 10^{1} |

90 | 9 × 10^{1} |

93 | 9.3 × 10^{1} |

98 | 9.8 × 10^{1} |

100 | 1 × 10^{2} |

157 | 1.57 × 10^{2} |

170.04 | 1.7004 × 10^{2} |

179 | 1.79 × 10^{2} |

230 | 2.3 × 10^{2} |

234 | 2.34 × 10^{2} |

250 | 2.5 × 10^{2} |

304 | 3.04 × 10^{2} |

400 | 4 × 10^{2} |

427 | 4.27 × 10^{2} |

500 | 5 × 10^{2} |

543 | 5.43 × 10^{2} |

604 | 6.04 × 10^{2} |

625 | 6.25 × 10^{2} |

673.5 | 6.735 × 10^{2} |

700 | 7 × 10^{2} |

763 | 7.63 × 10^{2} |

783.4 | 7.834 × 10^{2} |

785.1 | 7.851 × 10^{2} |

800 | 8 × 10^{2} |

816 | 8.16 × 10^{2} |

900 | 9 × 10^{2} |

923 | 9.23 × 10^{2} |

1,000 | 1 × 10^{3} |

1,200 | 1.2 × 10^{3} |

2,000 | 2 × 10^{3} |

2,000.82 | 2.00082 × 10^{3} |

2,012 | 2.012 × 10^{3} |

2,500 | 2.5 × 10^{3} |

3,000 | 3 × 10^{3} |

3,256 | 3.256 × 10^{3} |

3,427 | 3.427 × 10^{3} |

5,000 | 5 × 10^{3} |

5,008 | 5.008 × 10^{3} |

5,666.6 | 5.6666 × 10^{3} |

6,000 | 6 × 10^{3} |

6,725.72 | 6.72572 × 10^{3} |

8,000 | 8 × 10^{3} |

8,008 | 8.008 × 10^{3} |

9,000 | 9 × 10^{3} |

10,000 | 1 × 10^{4} |

25,000 | 2.5 × 10^{4} |

30,000 | 3 × 10^{4} |

40,000 | 4 × 10^{4} |

45,000 | 4.5 × 10^{4} |

46,959 | 4.6959 × 10^{4} |

65,000 | 6.5 × 10^{4} |

71,103 | 7.1103 × 10^{4} |

72,000 | 7.2 × 10^{4} |

80,109 | 8.0109 × 10^{4} |

86,500 | 8.65 × 10^{4} |

86,940 | 8.694 × 10^{4} |

89,000 | 8.9 × 10^{4} |

275,000 | 2.75 × 10^{5} |

380,000 | 3.8 × 10^{5} |

500,000 | 5 × 10^{5} |

908,110 | 9.0811 × 10^{5} |

31,571,012 | 3.1571012 × 10^{7} |

As you can see, very big and very small numbers are easier to read in the right column, without the need to count any string of zeroes.

They have been transformed into a simpler form.

## Summary

As you have learned, our calculator tool is a kind of Swiss Military knife built around scientific notation:

From scientific e notation to decimal notation calculator – it does it all.

The basic difference to an exponent calculator is that the **base** is always **10**.

To learn all about scientific notation visit our home page.

We wrap our scientific notation conversion calculator up with his image:

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Thanks for your visit! We are looking forward to seeing you here again soon.