Scientific Notation Calculator
Scientific notation calculator helps for those values which are very large or small and are difficult to write. It helps to write values more conveniently. It is commonly used in mathematics, physics, engineering, science, and chemistry, as it can help the user to simplify arithmetic operations. The calculator uses the scientific notation to express numbers in a form that is written as a base number a, multiplied by 10 raised to an integer exponent, n, denoted as a * 10ⁿ.
Calculator scientific calculates numbers both in decimals and integers notation compared to scientific notation. Here are some of the examples of decimal notation numbers express into scientific notation. 5 is a single decimal notation number, which can be represented in scientific notation as 5 × 10ⁿ where n is equal to 0. The same as another example of decimal notation for million is 1,000,000, which can be represented in scientific notation as 1 × 10^6.
Scientific notation calculator is also used for engineering notation, which is similar to the same calculator scientific notation except the power that is the exponent,n. The calculator scientific engineering uses SI-prefixes, which is restricted to multiples of 3 like 3, 6, 9, 12, etc. Some of the examples for engineering notation are given below;
For example, 10^6 would have the mega prefix, and 10^9 would have Giga prefix while the same in negative numbers 10^-3 would have a micro prefix, and 10^-6 would have nano prefix in scientific engineering notation.
In engineering notation, the decimal place of the number can be moved to convert scientific notation.
1.234 × 10^6 (scientific notation)
can be converted to:
123.4 × 10^4 (engineering notation).
Scientific notation depends on the decimal point whether it is moved to the right or the left of the original number. In the above process, an example has been shown how to convert a number into scientific notation.
Scientific Notation Calculator Online
Scientific notation Calculator online is a web tool used for mathematical, science, and engineering problems to perform addition, multiplication, subtraction, and division calculation and convert it into scientific notation. This online calculator performs a function between two numbers with respect to their exponential power (*10ⁿ).
This online scientific calculator shows multiple results for the operations of the required number. The online scientific calculator first shows the result in scientific notation then show it into E notation, And last show the result in decimal Notation. Scientific notation calculator online performs super fast on conversion the numbers into scientific, E, and decimal notation. It only just needs the values of exponent, which is mandatory in the required field.
Scientific Notation Conversion Calculator
There are some rules for converting a number into scientific notation, which must be remembered by everyone else. The first rule for scientific notation conversion is that the decimal point must lie between the first two non-zero digits. The number of digits in the significant is known as significant figures. Scientific notation conversion calculator converts these figures into scientific notation numbers before the multiplication symbol. For example, there are some conversion steps which show how to convert a number into scientific notation
Let’s suppose we want to convert the given number 0.00123 to scientific notation. The following steps would be used for the conversion of the scientific notation.
- First, place the decimal point between the two non-zero digits. i.e. 1.23
- Now count how many places the decimal was moved, which in this case is 3.
- Now check that weather the decimal point moved to the left or right side.
- If the decimal is transferred to the right side, the exponent is negative. The exponent will be positive if it is moved to the left side.
- Now use the exponent formula a * 10^n
- In this case, the number is (1.23 *10⁻³).
- You can compare your results with the scientific notation calculator.
Write in Scientific Notation Calculator
- To write a function in a scientific notation calculator, the user must be sure about the number in scientific notation, which is put correctly into your calculator. For that, the user needs to be familiar with exponents and the direction for the particular calculator.
Punch the number (the digit number) into your scientific notation calculator.
- Press the EE or EXP button. Try not to utilize the x (times) button!!
- Enter the type exponent number. Utilize the +/ – catch to change its sign.
- Treat this number ordinarily in every single consequent figuring.
All your numbers will be converted to the same power of 10, and the digit terms would be changed into the requested operator. To check by yourself, let multiply 5.0 *10³ times 8.0 *10³ on your scientific notation calculator. Your answer should be 4.0 *10^7.
Multiplying Scientific Notation Calculator
Multiplying a scientific notation calculator performs the product of two numbers with exponential power. Scientific notation calculators multiplied the digits in the usual way, and the exponents are added with the required field. The result of the given calculator would be changed as compared to the user inputs; in the result, there would be only one nonzero digit to the left of the decimal. Following is the multiplication function performed in the scientific notation calculator on the given values.
Example: (2.45 * 10^4)(4.32 * 10^6) = (1.0584 * 10^11).
Dividing Scientific Notation Calculator
The division and multiplication become easier when we have the same base for values since, in scientific notation, we have the same base, which is 10. Hence, the division is very simple in scientific notation. The exponent gets subtracted when the two values have the same base are divided. if we have to find division for two different scientific numbers, put the first number in the first box and the second number to be divided in the second box, change the sign of operator to the division sign and press calculate. for example 3^3/3^2 = (3/3)^(3-2) = 1^1 =1.
Adding Scientific Notation Calculator
The addition of scientific notation can be easily performed by using a scientific notation calculator when we have two different numbers, but their powers are the same, so the addition is simple; simply add the number, and the power will remain the same. But we face problems when the two numbers have different powers; this problem can be easily solved by using scientific notation calculator. Write the first number in the first box and the second number in the second box to be added, change the operator sign to plus sign and press the calculate button.
For example, to add 5 * 10^3 with 4 * 10^5, write 5 * 10^3 in the first box, and 4 * 10^5 in the second box, change the operator sign to plus and press the calculate button. It will give the required result, which is 4.05 * 10^5.
Subtracting Scientific Notation Calculator
In scientific notation calculator, we can easily use subtraction, and we can easily and quickly subtract one number from the other number. In this calculator, two different boxes are given for two different numbers to be deducted. Change the operator sign to the minus sign and then press the calculate button to get the required result.
For example, to subtract 2 * 10^2 from 4 * 10^4. Put the 4 * 10^4 in the first box and 2 * 10^2 in the second box, change the operator sign to the minus and press the calculate button, the required result is 3.98 * 10^4. By using this scientific notation calculator, we can also use the negative powers of 10 or negative exponent.
Convert to Scientific Notation Calculator
To convert standard numbers to scientific notation, we use a simple formula that is m * 10^n. m is used for those numbers which are written in standard form and n is used for the exponent or power of 10. to convert a number from standard form to scientific notation, the first rule is that put a decimal point after the first non-zero digit. The steps of the decimal point or the movement of the decimal point show the power of 10. if we move the decimal point towards the left, the power of 10 will be positive and if we move the decimal point towards the right the power of 10 will be negative.
The above discussion can be explained well by the help of a few examples.
- The scientific notation of 200 can be written as 2 * 10^2.
- The scientific notation of 54300 can be written as 5.43 * 10^4.
- The scientific notation of 2300000000 can be written as 2.3 * 10^9.
Similarly, the scientific notation for negative values can be written as
- The scientific notation for 0.0004 can be written as 4 * 10^-4.
- The scientific notation for 0.00000000045 can be written as 4.5 *10^-10.
Scientific Notation to Standard Form Calculator
The scientific notation calculator converts or gives results in three different forms, that is scientific form, e notation form, and in a standard form or decimal form. The standard form or decimal form means that the numbers are written in a conventional method or standard method of writing numbers.
By using a scientific notation calculator, we can quickly get the result in standard form. For example, the standard form of 4.56 * 10^2 is 456. The speed of light 3 * 10^8 m/s in standard form can be written as 300000000 m/s.
A mathematical operation is known as exponentiation. We write it as a^n. Here ‘a’ shows the base, and ‘n’ is the exponent. When the power ‘n’ is positive, the exponentiation results in repeated multiplication of the base ‘a’ up to ‘n’ times. For example, a^3 means a * a * a.
Exponent Law and Rules
- The exponent gets added, when the two values have the same base are multiplied. For example a^n * a^m = a^n+m i.e. 2^3 * 2^4 = 2^3+4 = 2^7.
- when the exponent is negative, we take the reciprocal of the base and raise its power or exponent to the positive integer. for example a^(-n) = 1/a^n i.e. 2^(-3) = 1/2^3 = 1/8.
- The exponent gets subtracted, when the two values have the same base are get divided. For example a^m/a^n = a^(m-n) i.e. 2^4/2^2 = 2^(4-2) = 2^2 =4.
- The exponent is get multiplied when an exponent comes just above on another exponent. for example, (a^m)^n = (a^m*n) = i.e. (2^3)^2 = (2^3*2) = 2^6 = 64.
- The exponent is get distributed to the bases when the two bases are get multiplied and are raised to the power of an exponent. for example, (a × b)n = a^n × b^n. i.e (2 * 5)^3 = 2^3 * 5^3 = 8 *125 = 1000
- when two bases are in the division and raised to an exponent, it is distributed to both of them. for example, (a / b)^n = a^n / b^n i.e. (2 / 3)^2 = 2^2 / 3^2 = 4 /9.
- The base remains the same when the exponent is 1. i.e., a^1 = a
- when the exponent is 0, it always gives 1 for any exponentiation. a^0 = 1.