Convert a number to clinical notation, E notation, or engineering notation or vice-versa making use of the clinical notation calculator.

You watching: What does 1.5e+9 mean

Decimal or Scientific Notation

Hint: usage either 5.2e+8 or 5.2 × 10^8 create to recurrent clinical notation.

*Scientific notation*, also called traditional develop, represents exceptionally big numbers or exceptionally small numbers in a shorter format. Numbers in clinical notation are an equation of a coreliable multiplied by 10 to the nth power.

Here’s an example:

1.5 × 102

The number to the left of the multiplication symbol is the coeffective, or periodically likewise called the mantissa. These are the significant digits in the number.

The number of digits in the coreliable will certainly vary relying on how many type of substantial numbers are in the number. Use our substantial numbers calculator to uncover substantial numbers or round a number to prepare for a conversion to clinical notation.

### Convert Using a Calculator

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

You have the right to likewise usage our exponent calculator to deal with the second part of the equation, then multiply the outcome by the coreliable.

**For example,** let’s convert 1.5 × 102 to decimal create.

1.5 × 102 = 1.5 × 1001.5 × 102 = 150

### Convert Scientific Notation without a Calculator

We’ve shown you how to convert a number expressed in scientific notation to a decimal by fixing, however this would certainly gain more challenging to carry out manually as the exponent gets bigger. There’s an alternate way to transform to decimal without fixing the equation.

If the exponent is positive, move the decimal allude in the coefficient to the appropriate one room for each value in the exponent.

For instance, if the exponent is 2, then relocate the decimal point to the best 2 spaces. If the exponent is negative, then relocate the decimal point to the left.

**For instance,** let’s convert 1.5 × 102 to a decimal utilizing this approach.

1.5 × 102 = 15.0 × 1011.5 × 102 = 150.0 × 1001.5 × 102 = 150.0

## How to Convert a Decimal to Scientific Notation

Converting a decimal number to scientific notation have the right to be done in a few basic measures.

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### 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 develop the beginning scientific notation equation for the decimal 475,000.475,000 = 475,000 × 100

### Tip Two: Move the Decimal Point

Now that we have actually an equation, the second action is to move the decimal suggest in the coreliable until tright here is one substantial digit to the left of the decimal allude. For each space the decimal point is moved to the left, boost the exponent by 1.

Continuing the instance above, relocate the decimal allude to the left and increment the exponent.

475,000 = 475,000.0 × 100475,000 = 47,500.0 × 101475,000 = 4,750.0 × 102475,000 = 475.0 × 103475,000 = 47.5 × 104475,000 = 4.75 × 105

### What About Numbers Less Than One?

The approach above functions for large numbers, yet the technique for taking care of small numbers much less than one is a little various.

Instead of relocating the decimal point to the left in the coefficient, the decimal point requirements to be moved to the right until one non-zero considerable digit is to the left of the decimal point. Because the number is acquiring bigger, we have to decrement a number from the exponent every time the decimal point is relocated.

**For instance,** let’s convert 0.00025 to clinical notation.

0.00025 = 0.00025 × 1000.00025 = 0.0025 × 10-10.00025 = 0.025 × 10-20.00025 = 0.25 × 10-30.00025 = 2.5 × 10-4

## How to Use Exponential Notation

*Exponential notation*, or E notation, is an additional form of clinical notation wright here the “× 10” part of the equation is replaced with an “e+”.

The “E” in E notation stands for exponential. This form is also frequently described as scientific E notation.

**For example,** let’s represent 1.5 × 102 in E notation.1.5 × 102 = 1.5e+2

## How to Convert to Engineering Notation

Not to be puzzled through E notation, *design 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 allude in the coefficient to the ideal and minimize the exponent till the exponent is a multiple of 3.

**For instance,** let’s reexisting 1.5 × 105 in E notation.1.5 × 105 = 15.0 × 1041.5 × 105 = 150.0 × 103

## Scientific Notation and Decimal Equivalents

Decimal numbers and also the identical values in clinical notation, E notation, and engineering notation.Decimal NumberScientific NotationE NotationEngineering Notation1 | 1 × 100 | 1E+0 | 1 × 100 |

1,000 | 1 × 103 | 1E+3 | 1 × 103 |

72,000 | 7.2 × 104 | 7.2E+4 | 72 × 103 |

1,349.12 | 1.34912 × 103 | 1.34912E+3 | 1.34912 × 103 |

0.000000435 | 4.35 × 10-7 | 4.35E-7 | 435 × 10-9 |

-7,500 | -7.5 × 103 | -7.5E+3 | -7.5 × 103 |

-0.00005234 | -5.234 × 10-5 | -5.234E-5 | -52.34 × 10-6 |

## Visual Guide to Convert to Scientific Notation

The infographic listed below demonstrates visually exactly how to convert a number to scientific notation.

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