Scientific Notation Converter

Scientific Notation Converter

Positive Values
. ×10


Negative Values
. ×10 _

This is a free online tool that converts scientific notations or numbers into the decimal numbers or standard forms. It is capable to convert both positive and negative numbers. Just enter you’re required notation and hit the “convert” button to get your answer in decimal number. Keep in mind, that there are two separate converters, 1st is for positive values while the 2nd is used for negative values, so be careful while during your conversion.

Use of Converter

  1. There are 3 separate input boxes.
  2. 1st is for decimal numbers before the point(.) digits.
  3. 2nd is for decimal numbers after the point(.) digits.
  4. 3rd is for the input of power 10.
  5. Use the positive for + and negative for – operations.
  6. For conversion press the “convert” button after inputting the digits.
  7. The “reset” button is used for the resetting of the converter.

Main Features and Functions

  1. Separate converter for positive and negative values.
  2. 100% tested and accurate conversion results.
  3. Fastest converter ever.
  4. Unlimited time of conversion capacity.
  5. A user-friendly interface.
  6. 1.0 Updated version.

Scientific Notation

It is the way of expression for a very large and a very small number to be written in standard or decimal form. It is mostly used by engineers, mathematicians, and scientists. For example, the 80,000,000 will be written as 8 ×107, the general formula is m ×10n. M is used for numbers written in standard form and n is used for the power of 10.

Definition

It is the mathematical expression that is used to write the big or large decimal numbers in fewer digits. For better understanding please follow and read the below section.

Scientific E Notation

The E notation is simply the same as the scientific notation, while the E letter represents the power of ten (×10n). Many calculators use the E notation formate to display their answer. The above converter can use for E notation while at the end, you will need to replace the ×10n into En. For example, 12.232×109 will be written as 12.232 E9 and so on.

Rules

The important Rules that are used and accepted universally are given below.

  1. The base is always 10.
  2. The exponent must be a non-zero digit.
  3. The absolute value of the coefficient is greater than or equal to 1 and must be less than 10.
  4. The coefficient may be positive or negative.
  5. The mantissa carries the rest of the significant digits.

The general notation for scientific is m ×10n. M is the coefficient and n is used for the power of 10.

How to Write

To write a number in scientific notation, let’s take an example of 64,000, now the below step for a proper conversion process.

Steps

  1. Move the decimal to the left after the first non-zero digit that is 6, i.e. 6.4
  2. Count the steps of the decimal that you move to the left, which are equal to 4.
  3. If you want to move the decimal to the left the power of 10 will be positive.
  4. But if you move the decimal to the right the power of 10 will be negative.

For example, the power of 10 will be 4 (positive), the required result can be obtained as. m ×10n, M is equal to 6.4 and n is equal to 4, 6.4 ×104 = 64000.

Examples

Please read the below examples to understand the conversion of the positive and negative values and as well as their differences.

Positive Values

  1. 600 can be written as 6×102.
  2. 4500000000 can be written as 4.5×109.
  3. 123000000 can be written as 1.23×108.

Negative Values

  1. 0.006 can be written as 6×10-3.
  2. 0.000000004 can be written as 4×10-9.
  3. 0.000002 can be written as 2 x 105.

Problems and Practice

It is the primary subject, and our goal is to solve all the problems that students are facing. Below are some problems with their solutions, which will practice you to solve all types of conversion.

Decimal or Whole Number to Scientific Notation

  1. 1001 = 1.001×103
  2. 53 = 5.3×101
  3. 6,926,300,000 = 6.9263×109
  4. -392 = -3.92×102
  5. 0.00361 = 3.61×10-3
  6. 6. 0.13592 = 1.3592×10-1
  7. -0.0038 = -3.8×10-3
  8. 0.00000013 = 1.3×10-7
  9. -0.567 = -5.67×10-1

Scientific Notation to Decimal or Standard Form

  1. 1.92×103 = 1,920
  2. 1.03×10-2 = 0.0103
  3. 3.051×101 = 30.51
  4. 8.862×10-1 = 0.8862
  5. -4.29×102 = -429
  6. 9.512×10-8 = 0.00000009512
  7. 6.251×109 = 6,251,000,000
  8. -6.5×10-3 = -0.0065
  9. 8.317×106 = 8,317,000
  10. 3.159×102 = 315.9

Worksheet

The worksheet is best for student practice and exam preparation, click here and download the scientific worksheet for the different level of grad and classes. You can do practice with the above converter as well.

Scientific Notation in Programming Languages

Python

There are four types of numbers in Pythons. The first one is “Integer,” the 2nd one is “Floating point,” the 3rd one is “Complex numbers,” and the 4th one is “Boolean.” The float value is used for the scientific notation in phyton, For example, 0.00000321 can be written as 3.21E-5, while the E is the exponent and you can you e or E it does not matter.

Matlab

Matlab and other programming languages use the E for the notation conversion. while the Matlab understand the value such as 10500e+5. The following are some examples of displaying numeric values.

>> format bank
>> a = 9.22222e+15
a = 9222220000000000.00
>> format hex
>> a = 9.22222e+15
a = 434061c7b591fc00
>> format longg
>> a = 9.22222e+15
a = 9.22222e+015

Informational and Biggest Notation Conversion

The Radius of Earth in Meters

In scientific notation, the radius of the earth in meters is equal to 6.37×106 meters or approximately 6.4×106 meters, and 6378100 or approximately 6370000 in standard form.

Speed of Light

The speed of light in scientific notation can be written as 2.99×108 m/s. Or it can also be written as 3×108 m/s. The speed of light in standard form is exactly 299792458 m/s or approximately 300000000 m/s.

Million or Mega

Mega is the scientific prefix for “1 million”, for example, one megabit means one million bit data. So for expression, the one million will be written as 1000000 = 106.

Billion

One billion in scientific notation is 1, and we place 10 to the power of 9. Means 1 billion is 1×109. Here we need to figure out the number we are raising 10. Then observe when to move the decimal point; we move 9 places to the left. If you move the decimal to the left, you will raise 10 to the power of n. If you move the decimal to the right, you will raise 10 to the power of -n.

Trillion

At 1 trillion, the non-zero digit is one. Here we drag the decimal point towards the end of the number to place it directly after 1. Now check out the resulting number is 1 so we can write as 1×1012 = 1000000000000.

Frequently Ask Questions

Archimedes, who discovered Scientific Notation was a mathematician and Greek inventor who was born in 287 B.C, in Syracuse, Greece and died in 212 B.C. Archimedes studied at the Egyptian city of Alexandria and then at the center of the scientific world.

256 in Scientific Notation = 2.56×102 where 2 is the order of magnitude.

  1. In this converter, three boxes are given for input values.
  2. The first box is used for digits before the decimal point.
  3. The second box is used for figures after the decimal point in scientific notation.
  4. The third box is used for the power of 10.
  5. By pressing the convert button, this will be changed to standard form or decimal form, which is the required result.
  6. For more values to be put in use the reset button, by pressing the reset button, you can enter the new values to be found.

Zeros after the decimal point and after figures are significant, in the number 0.2540, then 2, 5, 4, and last 0 are significant. Exponential digits in scientific notation are not significant; 1.12×106 has three significant digits, 1, 1, and 2.

To write 0.00001, we will have to move the decimal point five points to the right, which means multiplying by 10-5.

If your number in decimal form is 0.25. We move the decimal point, so there is only one non-zero digit in front of the decimal point. So, 0.25 becomes 02.5. The leading zero is not significant, so 02.5 becomes 2.5.

To write 500, move the decimal (understood to be at the end of the number) two spaces to the left so that only the 5 is to the left of the decimal, so for 500 is 5×102.

This comes from the fact that in the number 100, the decimal point is after the second zero, and to put this number into standard form, you must move the decimal point backward two places, giving you 1.00, then move the decimal point forwards two places, gives you 100. so for 100 is 1×102.