Scientific Notation Calculator and Converter

Instructions for use:

If the scientific notation is 0.1244107 x 10³, you must use 0.1244107e+3;
If the scientific notation is 14478 x 10^-3, you must use 14478e-3;
You will replace base 10 with the letter (e).

Scientific Notation 1:

Scientific Notation 2:

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Decimal to Scientific Notation

Scientific Notation to Decimal

	Scientific Notation	Decimal
Million in scientific notation	1 × 10⁶	1,000,000
10 Million in scientific notation	1 × 10⁷	10,000,000
100 Million in scientific notation	1 × 10⁸	100,000,000
Billion in scientific notation	1 × 10⁹	1,000,000,000
10 Billion in scientific notation	1 × 10¹⁰	10,000,000,000
100 Billion in scientific notation	1 × 10¹¹	100,000,000,000
Trillion in scientific notation	1 × 10¹²	1,000,000,000,000
10 Trillion in scientific notation	1 × 10¹³	10,000,000,000,000
100 Trillion in scientific notation	1 × 10¹⁴	100,000,000,000,000

	Scientific Notation	Decimal
Giga in scientific notation	10⁹	1,000,000,000
Mega in scientific notation	10⁶	1,000,000
Kilo in scientific notation	10³	1,000
Hecto in scientific notation	10²	100
Deka in scientific notation	10¹	10
Deci in scientific notation	10^-1	0.1
Centi in scientific notation	10^-2	0.01
Milli in scientific notation	10^-3	0.001
Micro in scientific notation	10^-6	0.000001
Nano in scientific notation	10^-9	0.000000001
Pico in scientific notation	10^-12	0.000000000001

Scientific Notation: Multiplication and Division

In every field of science, one must have to deal with numbers, the numbers can be in any format like the weight of the earth in kilograms is a very large number or mass of an electron is a very small number. The representation of these types of numbers is not easy.

Let suppose there is a number that has 22 zeros and written in this way

60220000000000000000000000

It’s not easy to read or understand that number easily. So there is a way known as a scientific notation that we can use to write very large or small numbers in an easier and understandable way.

Importance of scientific notation

In 1998 NASA launched the orbiter to find the data of climate change at mars but after three years the orbiter got lost and investigation on this matter shows that estimate of data was wrong because of two teams transfer their data in different units. The representation of the number in the standard form is very important because the accuracy of numbers matters, while reading too large or too small number we can make mistake while counting 0’s.

How to express numbers in scientific notation?

The numbers are written in product from like the first number is mantissa and second is the power of 10 exponents:

Any number = mantissa x 10^exponent

For example, if we take any large number of their scientific a notation will be like this way

7,000,000,000,000,000,000,000 = 7 × 10²¹

Here 7 is mantissa and 21 is exponent. Now we can see that while reading and writing of these types of numbers the chances of error become reduced and we can easily use these numbers in any paper writing work.

Before using scientific notation let’s find underlying theory. How we can find the different powers for 10?

10⁰ = 1
10¹ = 10
10³ = 1000

Here 10 power helps to find the zeros, like when power is 0 there is no zero follow 1, when power is 3 there are 3 zeros follows 1. Like in a similar way 10¹⁰⁰ = 1000….0 represent 100 zeros. Which is a very large number and is not easy to read so by scientific notation the representation of very big number become easy.

To express numbers in scientific notation, there should be only one digit remains to the left of the decimal point for this the decimal point move towards the left or right-hand side depending upon the number, either it is greater or less than zero. Multiplying by the different exponent of allow us to move the decimal place.

For example in

9.2867 × 10⁴ = 92876.00

the exponent of 10 is positive it allows decimal to move towards the right. While on the other hand, negative exponent move the decimal towards left

5 × 10^-15 = 0.000000000000005

But we keep one the thing in mind in the standard form of scientific notation that we have to left just one digit to the left of the decimal.

More advantage of scientific notation is that we can easily add, subtract, multiply, and divide large numbers. Let’s see how we can use this method to add numbers.

To add or subtract numbers in scientific notation the following steps are uses:

the exponents of 10 should keep the same in both terms.
After making the exponents of 10 the same, we can add or subtract the numbers.
Lastly we should adjust the answer according to scientific notation.

Add Scientific Notation: (5.7 × 10⁴) + (2.25 × 10⁵)

Adjust the power of large exponent according to the small power.

5.7 × 10⁴ ) + (2.25 × 10¹ × 10⁴)

Now group the numbers

(5.7 + 2.25 × 10¹) × 10⁴
(5.7 + 22.5 ) × 10⁴
28.2 × 10⁴

Now adjust number according to standard form of scientific notation

(2.82 × 10¹) × 10⁴ = 2.82 × 10⁵

In the similar way we can subtract two quantities.

Subtract Scientific Notation: (6.67 × 10⁸ ) – (8.4 × 10⁶)

Adjust the power of large exponent according to the small power.

(6.67 × 10² × 10⁶) – (8.4 × 10⁶)

Now group the numbers

(667 – 8.4) × 10⁶
658.6 × 10⁶

Now adjust number according to standard form of scientific notation

(6.58 × 10²) × 10⁶ = 6.58 × 10⁸

All numbers in scientific notation have the base 10 so we can easily multiply and divide them:

Multiply and divide two numbers, we multiply or divide their mantissas, add and subtract the power of exponents respectively.
In both cases, we should convert a number in the standard form of scientific notation.

For example:

Multiply Scientific Notation: (6.87 × 10¹²) × (4.102 × 10⁶)

Multiply the mantissas of each quantity

6.87 × 4.102 = 28.187

Now add the powers of exponents

(10¹² × 10⁶) = 10¹⁸

Write the number in standard form of scientific notation

28.187 × 10¹⁸ = 2.8187 × 10¹ × 10¹⁸ = 2.8187 × 10¹⁹

Let’s try example for division:

Divide Scientific Notation: (2.04 × 10⁶) ÷ (7.82 × 10²)

Divide the mantissas of each quantity

2.04 ÷ 7.82 = 0.26086

Now subtract the powers of exponents

(10⁶ × 10²) = 10⁴

Write the number in standard form of scientific notation

0.26086 × 10⁴ = 2.6086× 10^-1 × 10⁴ = 2.6086 × 10³

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