Scientific Notation Calculator: Convert Online

The Scientific Notation Calculator will assist you in converting large and small numbers to scientific notation quickly and accurately. This is a free online tool.

Scientific notation can be used in many areas such as maths, physics, chemistry, engineering, astronomy and more. This can make reading, writing, comparing and calculating numbers much easier.

For example, 150,000,000 can be written as \\(1.5 \\times 10^8\\), while the very small number 0.0000042 can be expressed as \\(4.2 \\times 10^{-6}\\).

Scientific notation can be used to help shorten the number and make it much clearer to see. This is useful when dealing with large measurements and tiny measurements.

When using our free Scientific Notation Calculator we can convert numbers into scientific notation with ease. You enter in a number and the calculator will assist you. Depending on what features are available you can also convert scientific notation back into a normal decimal.

This can help students in the USA with their maths and science homework, exam revision and problem solving.

Overall this can save you time whether you are a student, teacher, researcher or professional.

How to use the Scientific Notation Calculator

Using the scientific notation converter online is an easy process and you don’t need any advanced mathematical knowledge.

Steps to follow:

1.Enter your number into the calculator. You could be entering in a large or small number or a normal number.

2.Select which conversion type you want to use. This can be either converting to scientific notation or vice versa.

3.Hit the calculate or convert button.

4.The number will then be converted into scientific notation.

5.Look at the power of 10 used. This will tell you how many decimal places the number has.

6.Reset and enter a new number. If needed you can reset the calculation and enter a new number.

Example

We want to convert 45,000 into scientific notation.

Enter:

45000

Result:
4.5 x 10 4

This means that the decimal has been moved 4 places to the left.

Scientific Notation Calculator Formula

Scientific notation uses coefficients and powers of 10.

Scientific Notation:
\\(a \\times 10^n\\)
\\(4.5 \\times 10^{4} = 45000\\)
Coefficient
Exponent
Decimal moved 4 places to the rightnew decimal45000
Feedback
Where,
a = Coefficient: This should be a number ≥1 and <10 if the number is non zero.
10 = Base: This is the base number used.
n = Exponent: This is an integer used to show how many places the decimal has been moved.

Positive Exponents

Positive exponents are used when the number is ≥10.

Example:

6,500,000=6.5 x 10 6

This means that the decimal has been moved 6 places to the right.

Negative Exponents

Negative exponents are used for non-zero numbers that are less than 1.

Example:

0.00032=3.2 x 10-4

The negative exponent shows that the decimal has been moved 4 places to the left.

Zero Exponents

If the number is multiplied by \\(10^0\\) it will remain the same as anything multiplied by 1 is itself.

10^0=1
Example:
7.5 x 10 0=7.5

This will help you convert between scientific notation and normal decimal numbers.

Example Calculation

Let’s look at how to convert a large number into scientific notation.

Convert 72,500,000 into scientific notation.

Write down the number:

72,500,000

Move the decimal:

We place the decimal after the first non-zero digit.

7.25

Count how many decimal places have been moved:

The decimal has been moved 7 places.

Use the formula:

7.25 x 10 7
Answer: 7.25 x 10 7

Small Number Example

Convert 0.000056 into scientific notation.

Write down the number:

0.000056

Move the decimal 4 places:

5.6

As the number was less than 1 we need to use a negative exponent:

5.6 x 10-5

Answer:

5.6 x 10-5

Understanding your answer

The answer given from the Scientific Notation Calculator will give you two pieces of information.

Example:

3.45 x 10 6

Coefficient: 3.45

Base: 10

Exponent: 6

Normal Number: 3,450,000
T

he coefficient refers to the significant figures within the number. The exponent shows how far the decimal has been moved.

Positive Exponent: The number is usually ≥10.

Negative Exponent: Non-zero number less than 1.

Zero Exponent: The coefficient is unchanged.

Coefficient: This will show the significant figures of the original number.

Normal Number: This will show the value using normal decimal numbers.

For example, \\(8.2\\times10^{-3}\\) would be 0.0082.

This will help you understand the scientific measurements.

Factors affecting the result

There are a few factors that will affect the scientific notation.

Original Number

The original number will determine how big the coefficient and exponent will be. Very large numbers will usually use positive exponents. Whereas very small non-zero numbers will use negative exponents.

Decimal

The decimal place will determine how big the exponent is. If the decimal isn’t in the correct place this may alter the value.

Significant Figures

Significant figures are the meaningful numbers within a measurement. This can impact how the coefficient is shown.

Rounding

Sometimes Scientific Notation Calculators will round the number to a certain number of decimal places. For example, it may round 3.4567 to 3.46.

Negative Numbers

Negative numbers will still be negative after conversion. For example,

-45,000 = -4.5 x 10 4.

Zero

Zero is a special case as it can’t be represented using scientific notation.
Incorrect decimal separators, extra characters or using incorrect notation can cause issues when converting. You should enter the number using a supported format.

Benefits of a Scientific Notation Calculator

The Scientific Notation Calculator can offer a few benefits.

• Save Time: Converting large and small numbers can take a long time. Using this tool will give you quick results.
• Supports Students: Students studying algebra, chemistry, physics and general science can use this tool to help with their homework. This can help them check their answers.
• Useful for Scientific Research: Researchers often have to deal with very large and very small measurements. Using scientific notation can help them organise and communicate these values.
• Helps with Physics: Physics deals with measurements such as the speed of light, atomic sizes, energy and distances in space. Using scientific notation can help with calculations.
• Useful for Chemistry: Many calculations in chemistry deal with very small measurements. This includes the mass of atoms, size of molecules and particles.
• Improves Maths Knowledge: By comparing the normal number with the scientific notation you can understand how the decimal place works, powers of 10 and exponents.
• No Manual Error: As the numbers are being converted automatically there is less chance of miscalculating how many decimal places have been moved.

Most Scientific Notation Calculators available online will work on desktops, laptops, tablets and phones.

Accuracy, Assumptions & Limitations

As long as the original number was entered correctly and the Scientific Notation Calculator can support the input, you can get accurate conversions.

There are a few assumptions and limitations to consider.

• Correct Input: The calculator will depend on the number you enter. If you enter incorrect digits or decimal, you will get an incorrect answer.
• Rounding: Some tools will round the coefficient to a certain number of significant figures. Therefore this may change the value slightly.
• Significant Figures: Scientific notation won’t automatically know how accurate the measurement was from the original number. This will depend on how many significant figures were in the original measurement.
• Zero: Zero is a special case as you can’t have a coefficient between 1 and 10 for the normalised scientific notation.
• Negative Numbers: Negative numbers are acceptable, however you need to ensure the number remains negative.
• Large & Small Numbers: Very large or very small numbers may be out of the acceptable range for some calculators.
• Different Display: Some devices may show scientific notation in a different format. For example, 4.5E+8.

Always double check the input, exponent and accuracy of the conversion if it is an important calculation for science, academic or engineering purposes.

FAQs

What is a Scientific Notation Calculator?

A Scientific Notation Calculator is an online tool that can be used to convert large and small numbers into scientific notation. This shows numbers in a form of a coefficient and power of 10 to make calculations easier to read.

Is it free to use?

Yes! There are many free Scientific Notation Calculators online. You can easily convert between normal decimal notation and scientific notation.

How do I convert a number to scientific notation?

Move the decimal so that there is only one non-zero digit before the decimal. Count how many places you have moved the decimal. If you moved it to the left use a positive exponent and if you moved it to the right use a negative exponent.

What is the difference between positive and negative exponents?

The positive exponent means that the number is larger whereas the negative exponent means it is a non-zero number less than 1. For example, \\(4.2 \\times 10^{-6}\\)0 whereas \\(4.2 \\times 10^{-6}\\)1.

Can I use a Scientific Notation Calculator on my phone?

Yes! Most Scientific Notation Calculators online should work on your smartphone, tablet, laptop and desktop. Just open up a modern browser and you should be able to use the calculator.