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Scientific Notation Calculator

Scientific Notation Calculator
enter numbers or scientific notation
 
Answer:
= 4.875 × 105
(scientific notation)

= 4.875e5
(scientific e notation)

= 487.5 × 103
(engineering notation)
(thousand; prefix kilo- (k))


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Calculator Use

Use this calculator to add, subtract, multiply and divide numbers in scientific notation, E notation or engineering notation. Answers are provided in three formats: scientific notation, E notation and engineering notation. You can also do operations on whole numbers, integers, and decimal numbers and get answers in scientific notation.

If you mark the check box the calculator automatically determines the number of significant figures in the answer. If you do not mark the check box, answers may contain more digits than are signficant.

Caution: See note regarding significant figures calculations.

Example Calculations

Use the links below to load a sample calculation into the calculator. In each example the input forms are different, but they all produce the same answers in scientific notation and E notation.

Standard Notation

Standard notation is the usual way to write numbers, with or without commas and decimals. This example calculation solves the addition problem 122500 + 3655. Click on the link and then refer to the calculator above. Note that the inputs are standard notation numbers. The answers are formatted in scientific notation and E notation.

122500 + 3655 = 1.26155 x 105

Scientific Notation

In scientific notation a large number is converted to an equivalent decimal number between 1 and 10, multiplied by 10 raised to some power. Very small numbers are converted to an equivalent decimal number between 1 and 10, multiplied by 10 raised to some negative power. In this example scientific notation calculation we're solving 1.225 × 105 + 3.655 × 103:

1.225 × 105 + 3.655 × 103 = 1.26155 x 105

E Notation

E notation is also known as exponential notation. E notation is the same as scientific notation where a decimal number between 1 and 10 is multiplied by 10 raised to some power. In E notation the "times 10 raised to a power" is replaced with the letter e in either uppercase or lowercase. The number after the "e" indicates how many powers of 10. In this example calculation we're adding 1.225e5 and 3.655e3:

1.225e5 + 3.655e3 = 1.26155e5

Note: Doing Math With Significant Figures

There are some cases where you would not want to auto-calculate significant figures. If your calculation involves a constant or an exact value as you might find in a formula, do not check the "auto-calculate" box.

For example, consider the formula for diameter of a circle, d = 2r, where diameter is twice the length of the radius. If you measure a radius of 2.35, multiply by 2 to find the diameter of the circle: 2 * 2.35 = 4.70

If you use this calculator for the calculation and you mark the "auto-calculate" box, the calculator will read the 2 as one significant figure. Your resulting calculation will be rounded from 4.70 to 5, which is clearly not the correct answer to the diameter calculation d=2r.

You can think of constants or exact values as having infinitely many significant figures, or at least as many significant figures as the least precise number in your calculation. Use the appropriate number of significant figures when you input exact values in this calculator. In this example you would want to enter 2.00 for the constant value so that it has the same number of significant figures as the radius entry. The resulting answer would be 4.70 which has 3 significant figures.

Additional Resources

See our Rounding Significant Figures Calculator for more information on significant figures.

See the Scientific Notation Converter to convert a number into scientific notation or E notation.

If you need a scientific calculator see our resources on scientific calculators.

The Math Forum: Ask Dr Math Rules for Significant Figures and Decimal Places



 

Cite this content, page or calculator as:

Furey, Edward "Scientific Notation Calculator"; from https://www.calculatorsoup.com - Online Calculator Resource.

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