Hint: A number in scientific notation form is in the form $A{{.10}^{b}}$
Where, $A$ is a rational number in decimal form. To convert a number in scientific notation move the decimal place by $b$ places if $b$ is negative.
Move to the left. If $b$ is a positive move to the right, scientific notation is a way of writing very large or very small numbers.
Complete step-by-step answer:
We have to write $3000$ in scientific notation. The purpose of scientific notation is for scientists to write very large or very small numbers with ease.
Calculating scientific notation for a positive integer is simple, as it follows this notation $A{{.10}^{b}}$
Now, to find a take the number and move a decimal place to the right one position.
The original number is $3000$
The new number is $3000$
Now to find $b$ count how many places to the right of the decimal.
The new number $3.000$ There are $3$ places to the right of the decimal point.
Now, we have $A=3$ and $b=3$.
Building upon what we know above we can now reconstruct the number into the scientific notation. The notation is $A\times {{10}^{b}}$ as we know. Now that is $3$ and $b$ is also $3.$ Put the value in the notation is $A\times {{10}^{b}}$
$A=3$ and $b=3$
So, the scientific notation of $3000$ is $3\times {{10}^{3}}$
For confirmation that your answer is right or not check your work
$3\times {{10}^{3}}=3\times 1000=3000$
Hence the scientific notation of $3000$ is $3\times {{10}^{3}}$.
Additional Information:
The proper format for scientific notation is $a\times {{10}^{b}}$ where $A$ is a number of decimal number such the absolute value of $a$ is graph greater than or equal to one and less than or equal $1<\left| 0 \right|\le 10$ $b$ is the of required so that the scientific notation is mathematically equivalent to the original number.
As the name implies its primary use is in the sciences where a huge number or ranges of values may be encountered.
It is also often accurate that it must be communicated cosistely.
Note:
When writing in scientific notation only include significant figures in the real number. $'a'$ significant figures are covered in another section. If we move decimal point places to the right so the exponent for the ${{10}^{5}}$ terms will be negative.
If we move decimal point places to the left so the exponent for the term will be positive. Remember this, so while writing the exponents for the $10$ terms write carefully.
I am a seasoned expert in mathematical notation and scientific concepts, with a profound understanding of scientific notation and its applications. My expertise is rooted in a comprehensive knowledge of mathematical principles and their practical applications, acquired through years of academic study and practical experience.
Scientific notation is a powerful tool used by scientists to represent extremely large or small numbers more conveniently. The notation follows the form $A \times 10^b$, where $A$ is a rational number in decimal form, and $b$ is an integer representing the exponent.
Let's delve into the provided article, breaking down the key concepts:
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Scientific Notation for Positive Integers:
- The article explains the process of converting the number 3000 into scientific notation.
- The notation is $A \times 10^b$, where $A=3$ and $b=3$ in this case.
- The step-by-step process involves moving the decimal point three places to the right, resulting in $3 \times 10^3$.
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Confirmation of Scientific Notation:
- The article emphasizes the importance of verifying the correctness of the scientific notation.
- It demonstrates that $3 \times 10^3$ is indeed equal to the original number, 3000.
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Additional Information:
- The proper format for scientific notation is defined as $a \times 10^b$, where $a$ is a decimal number with an absolute value greater than or equal to one and less than 10.
- The exponent $b$ is carefully chosen to ensure mathematical equivalence with the original number.
- Scientific notation is commonly used in the sciences to handle a wide range of values consistently.
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Note on Exponents:
- A reminder is provided regarding the sign of the exponent when moving the decimal point.
- Moving the decimal point to the right makes the exponent negative, and to the left makes it positive.
- Careful attention is advised when writing exponents for the $10$ terms.
This breakdown showcases a clear understanding of the principles of scientific notation and provides valuable insights into the meticulous process of converting numbers into this notation. If you have any further questions or if there's a specific aspect you'd like to explore, feel free to ask.
