To rewrite the number [tex]\( 13,180,000,000 \)[/tex] in scientific notation, follow these steps:
1. Identify the Significant Figures:
The number [tex]\( 13,180,000,000 \)[/tex] has significant figures. We need to identify the most significant digits, which are the leading non-zero digits, here being 1318.
2. Place the Decimal Point:
Place a decimal point after the first digit to form a number between 1 and 10. For 1318, this would be [tex]\( 1.318 \)[/tex].
3. Determine the Exponent:
Count how many places you need to move the decimal point to convert the original number to the form you have now. In [tex]\( 13,180,000,000 \)[/tex], the decimal point is originally after the last zero. This means you need to move the decimal point 10 places to the left to get from [tex]\( 13,180,000,000 \)[/tex] to [tex]\( 1.318 \)[/tex].
4. Express in Scientific Notation:
Combine the significant figures with the power of 10 that reflects the decimal shift. Since we moved the decimal 10 places to the left, the exponent will be positive 10.
Therefore, the number [tex]\( 13,180,000,000 \)[/tex] written in scientific notation is:
[tex]\[
1.32 \times 10^{10}
\][/tex]
Thus, the scientific notation form of [tex]\( 13,180,000,000 \)[/tex] is:
[tex]\[
1.32e+10
\][/tex]
