# Scientific Notation Calculator and Decimal Conversion

Enter a decimal number in the form below to convert it to scientific notation, E notation, or engineering notation. You can also enter a number in scientific notation to convert to a decimal.

## Solution:

### Scientific Notation

^{8}

### E Notation

### Engineering Notation

^{6}

### Decimal Notation

## On this page:

- Calculator
- How to Convert a Number in Scientific Notation to Decimal Form
- Converting Scientific Notation to a Decimal Without a Calculator
- How to Convert a Decimal Number to Scientific Notation
- Converting to E Notation
- Converting to Engineering Notation
- Equivalent Values in Decimal and Scientific Notation
- Infographics

## How to Convert a Number in Scientific Notation to Decimal Form

**Scientific notation**, or standard form, is a way of representing very large numbers or very small numbers in a shorter format. Numbers in scientific notation are actually an equation of a coefficient multiplied by 10 to the nth power.

Here’s an example:

1.5 × 10^{2}

To convert a number that is currently in scientific notation to decimal notation simply solve the equation. To solve, multiply the coefficient by ten to the nth power.

**For example,** let’s convert 1.5 × 10^{2} to decimal form.

1.5 × 10^{2} = 1.5 × 100

1.5 × 10^{2} = 150

### Converting Scientific Notation to a Decimal Without a Calculator

We’ve showed you how to convert a number expressed in scientific notation to a decimal by solving, but this would get more difficult to do manually as the exponent gets larger. There’s an alternate way to convert to a decimal without solving the equation.

If the exponent is positive, move the decimal point in the coefficient to the right one space for each value in the exponent. For instance, if the exponent is two then move the decimal point to the right two spaces. If the exponent is negative then move the decimal point to the left.

**For example,** let’s convert 1.5 × 10^{2} to a decimal using this method.

1.5 × 10^{2} = 15.0 × 10^{1}

1.5 × 10^{2} = 150.0 × 10^{0}

1.5 × 10^{2} = 150.0

## How to Convert a Decimal Number to Scientific Notation

Converting a decimal number to scientific notation can be done in a few simple steps.

### Step One: Create Initial Equation

First, create an equation with the initial decimal being the coefficient multiplied by 10 to the power of 0.

**For example,** let’s create the starting scientific notation equation for the decimal 475,000.

475,000 = 475,000 × 10^{0}

### Step Two: Move the Decimal Point

Now that we have an equation, the second step is to move the decimal point in the coefficient until there is 1 significant digit to the left of the decimal point. For each space the decimal point is moved to the left, increase the exponent by 1.

Continuing the example above, move the decimal point to the left and increment the exponent.

475,000 = 475,000.0 × 10^{0}

475,000 = 47,500.0 × 10^{1}

475,000 = 4,750.0 × 10^{2}

475,000 = 475.0 × 10^{3}

475,000 = 47.5 × 10^{4}

475,000 = 4.75 × 10^{5}

### What About Numbers Less Than One?

The method above works for large numbers, but the method for handling small numbers that are less than one is a little bit different.

Instead of moving the decimal point to the left in the coefficient, the decimal point needs to be moved to the right until one non-zero significant digit is to the left of the decimal point. Because the number is getting larger we need to decrement a number from the exponent every time the decimal point is moved.

**For example,** let’s convert 0.00025 to scientific notation.

0.00025 = 0.00025 × 10^{0}

0.00025 = 0.0025 × 10^{-1}

0.00025 = 0.025 × 10^{-2}

0.00025 = 0.25 × 10^{-3}

0.00025 = 2.5 × 10^{-4}

## Converting to E Notation

**E notation** is another form of scientific notation where the “× 10” part of the equation is replaced with an “e+”.

The “E” in the name stands for exponential. This form is also commonly referred to as scientific E notation.

**For example,** let’s represent 1.5 × 10^{2} in E notation.

1.5 × 10^{2} = 1.5e+2

## Converting to Engineering Notation

Not to be confused with E notation, **engineering notation** is an alternate form of scientific notation where the exponent is a multiple of 3.

To convert scientific notation to engineering notation move the decimal point in the coefficient to the right and reduce the exponent until the exponent is a multiple of 3.

**For example,** let’s represent 1.5 × 10^{5} in E notation.

1.5 × 10^{5} = 15.0 × 10^{4}

1.5 × 10^{5} = 150.0 × 10^{3}

## Equivalent Values in Decimal and Scientific Notation

Decimal Number | Scientific Notation | E Notation | Engineering Notation |
---|---|---|---|

1 | 1 × 10^{0} |
1E+0 | 1 × 10^{0} |

1,000 | 1 × 10^{3} |
1E+3 | 1 × 10^{3} |

72,000 | 7.2 × 10^{4} |
7.2E+4 | 72 × 10^{3} |

1,349.12 | 1.34912 × 10^{3} |
1.34912E+3 | 1.34912 × 10^{3} |

0.000000435 | 4.35 × 10^{-7} |
4.35E-7 | 435 × 10^{-9} |

-7,500 | -7.5 × 10^{3} |
-7.5E+3 | -7.5 × 10^{3} |

-0.00005234 | -5.234 × 10^{-5} |
-5.234E-5 | -52.34 × 10^{-6} |

## Infographics

You are free to use and share these infographics that summarize the steps shown above.