Final answer:
The standard number for thirty-six and fifteen hundredths is 36.15. Large numbers, such as 306,000,000, are written in scientific notation as 3.06 × 10^8, and small numbers, like 0.0000558, are written as 5.6 × 10^-5, both using significant figures to indicate precision.
Step-by-step explanation:
The standard number for thirty-six and fifteen hundredths is written as 36.15 in standard notation.
Scientific Notation for Large Numbers
For the number 306,000,000, it can be written in scientific notation as 3.06 × 108 to the proper number of significant figures, which in this case is three (3, 0, and 6).
Scientific Notation for Small Numbers
Similarly, the number 0.0000558 written in scientific notation with two significant figures would be 5.6 × 10-5. This indicates that we have rounded the figure to two significant digits and used an exponent to indicate the placement of the decimal point.
Significant figures play a critical role in scientific notation by determining the precision of the number represented. For example, writing 1300 in scientific notation as 1.3 × 103 includes only the significant figures.