Answer :
Sure! Let's go through the process of converting the number [tex]\(3,163,100,000\)[/tex] into scientific notation step by step.
### Step-by-Step Solution:
1. Identify the Number:
We start with the number [tex]\(3,163,100,000\)[/tex].
2. Place the Decimal Point:
To express this in scientific notation, we need to place the decimal point after the first significant digit. In this number, the first significant digit is [tex]\(3\)[/tex]. So, we reposition the decimal point to get [tex]\(3.163100000\)[/tex].
3. Count How Many Places the Decimal Moved:
Initially, the decimal point is at the end of the number (after all the zeros). Moving the decimal point to after the first digit (3), we see it has shifted 9 places to the left. This count (9) will be the exponent in the scientific notation.
4. Express in Scientific Notation:
In scientific notation, a number is written as:
[tex]\[
a \times 10^b
\][/tex]
where [tex]\(a\)[/tex] is a number between 1 and 10, and [tex]\(b\)[/tex] is an integer.
For our number [tex]\(3,163,100,000\)[/tex], it becomes:
[tex]\[
3.1631 \times 10^9
\][/tex]
5. Round if Required:
Sometimes, scientific notation is rounded to a few significant digits. Here, if we round [tex]\(3.1631\)[/tex] to three significant digits, it becomes [tex]\(3.16\)[/tex].
Thus, the number [tex]\(3,163,100,000\)[/tex] in scientific notation, rounded to three significant digits, is:
[tex]\[
3.16 \times 10^9
\][/tex]
### Final Answer:
[tex]\( 3,163,100,000 \)[/tex] in scientific notation is [tex]\( 3.16 \times 10^9 \)[/tex].
This completes our conversion process.
### Step-by-Step Solution:
1. Identify the Number:
We start with the number [tex]\(3,163,100,000\)[/tex].
2. Place the Decimal Point:
To express this in scientific notation, we need to place the decimal point after the first significant digit. In this number, the first significant digit is [tex]\(3\)[/tex]. So, we reposition the decimal point to get [tex]\(3.163100000\)[/tex].
3. Count How Many Places the Decimal Moved:
Initially, the decimal point is at the end of the number (after all the zeros). Moving the decimal point to after the first digit (3), we see it has shifted 9 places to the left. This count (9) will be the exponent in the scientific notation.
4. Express in Scientific Notation:
In scientific notation, a number is written as:
[tex]\[
a \times 10^b
\][/tex]
where [tex]\(a\)[/tex] is a number between 1 and 10, and [tex]\(b\)[/tex] is an integer.
For our number [tex]\(3,163,100,000\)[/tex], it becomes:
[tex]\[
3.1631 \times 10^9
\][/tex]
5. Round if Required:
Sometimes, scientific notation is rounded to a few significant digits. Here, if we round [tex]\(3.1631\)[/tex] to three significant digits, it becomes [tex]\(3.16\)[/tex].
Thus, the number [tex]\(3,163,100,000\)[/tex] in scientific notation, rounded to three significant digits, is:
[tex]\[
3.16 \times 10^9
\][/tex]
### Final Answer:
[tex]\( 3,163,100,000 \)[/tex] in scientific notation is [tex]\( 3.16 \times 10^9 \)[/tex].
This completes our conversion process.
