Scientific Notation Converter
Welcome to our scientific notation converter, where you can convert a decimal to scientific notation or vice versa. The scientific notation conversion is simple, but you're not the only one confounded by it once in a while, and that's where our converter can help!
In the following article, we aim to convey the fundamentals of this topic, including:
- What is scientific notation?
- How to convert numbers into scientific notation?
- Converting scientific notation to decimal form.
What is scientific notation?
Scientific notation is a convenient way of writing large numbers or numbers with too many decimal places. In scientific notation, we express numbers in the form:
- - The significand or mantissa, a real number coefficient such that ; and
- - An integer exponent.
For example, consider the number 0.0000272. Writing it this way makes it hard to read it correctly. Besides, using this form in calculations can be a hassle, too. Instead, expressing the number in its scientific form, 2.72 × 10-5, makes our life easier.
8 × 100
2.42 × 103
-6 × 10-1
4.2182 × 102
8.24 × 10-8
How do you convert numbers into scientific notation?
To convert a decimal number into scientific notation, follow these steps:
Move the decimal point from its original place to after the first non-zero digit in the decimal number. This new number is the mantissa m.
Count the number of decimal places the point was moved. This shall be the exponent x of the number.
The exponent x is positive if the decimal point is moved to the left and negative if the point is moved to the right.
Multiply the mantissa with 10x to get the scientific notation: m × 10x.
Consider the number 0.00007248. Let's use the above method to convert this number into scientific notation:
- Move the decimal point after the first non-zero digit: 7.248.
- Count the number of decimal places we moved the point: 5.
- Since we moved the decimal point to the right, the exponent is negative: -5.
- Multiply 7.248 with 10-5 to get the scientific notation of 0.00007248 as 7.248 × 10-5.
Test your understanding of scientific notation conversion: Convert the numbers 866.452 and 0.0001054 into scientific notation. You can verify your answers with our scientific notation converter.
Calculating decimal notation from scientific notation
Now that you've learned how to convert numbers into scientific notation let's learn to convert a number from scientific notation to standard form with an example. Consider the number 6.045 × 10-9:
- Note the sign of the exponent:
- If the exponent is positive, we move the decimal point to the right.
- If the exponent is negative, we move the decimal point to the left.
- Move the decimal point 9 places to the left to get: 0.000 000 006 045.
Our scientific notation converter can also calculate scientific notation to decimal conversion for you!
Using this scientific notation converter
Using our calculator to convert to scientific notation and vice versa is simple:
- Enter any number you wish to convert into scientific or decimal form, and the calculator will give you the following results:
- The scientific notation of the number.
- The number's decimal notation.
Inputting numbers in the scientific form: You have two ways to enter a number in its scientific form:
Using e: You can enter a number in scientific form using the alphabet
efollowed by the exponent value. For example, you can input 6.023 × 10-24 as 6.023e-24. If no exponent follows the alphabet
e, the calculator will assume
eas the Euler's constant!
Using advanced mode: Click on the advanced mode button and select the exponent part from the units drop-down list first. Then, enter the mantissa in the same field. For example, to enter 6.023 × 10-24, first select the exponent 10-24 from the list in the scientific notation field, and then enter 6.023 in the same field.
🔎 Significant figures: In our advanced mode, you also have the option to specify the significant figures! After entering the number, specify its significant digits in the field labeled significant figures. By default, it is set to 10.
Other related tools
Want to express your number in scientific e-notation? Or are you looking for engineering notation? Omni has the complete package for you to try next:
What is the scientific notation of 10.023?
In scientific notation, 10.023 is written as 1.0023 × 101. To make this conversion yourself, follow these simple steps:
- Move the decimal point after the first non-zero digit: 1.0023.
- Count the number of decimal places we moved the point: 1.
- Since we moved the decimal point to the left, the exponent is positive: 1.
- Multiply 1.0023 with 101 to get the scientific notation of 10.023 as 1.0023 × 101.
- Verify with our scientific notation converter.
How do I multiply two numbers in scientific notation?
Multiplying two numbers in scientific notation, say m × 10a and n × 10b is simple:
- Multiply the mantissa of the two scientific numbers: m × n.
- Write their product in scientific form as well: m × n = p × 10c.
- Add the exponents a, b, and c to get the exponent of the final product.
- Write the answer in its scientific form: p × 10(a+b+c).