Exercise 5: Significant Digits and Scientific Notation Part 1: Determine the number of significant digits in each number, and write the specific significant digits. 1. 405000 2. 0.0098 3. 39.999999 4. 13.00 5. 80,000,089 6. 55,430.00 7. 0.000033 8. 620.03080 Part 2: Convert each regular number into scientific notation. 1. 70,000,000,000 2. 0.000000048 3. 67,890,000 4. 70,500 5. 450,900,800 6. 0.009045

[tex]1. \hspace{3} 70000000000 = 7\times10^{10}\\2. \hspace{3} 0.000000048 = 4.8\times10 ^{-8}\\3. \hspace{3} 67890000 = 6.789\times10^7\\4. \hspace{3} 70500 = 7.05\times10^4\\5. \hspace{3} 450900800 = 4.509008\times10^8\\6. \hspace{3} 0.009045 = 9.045\times10^{-3}\\[/tex]

Step-by-step explanation:

The significant digits in a real number refer to the digits that are held in the gutter to determine their accuracy. That is, those relative values that could be determined with certainty. Therefore, the answers are:

1. 405000: Number of significant digits 3. 405

2. 0.0098: Number of significant digits 2. 98

3. 39.999999: Number of significant digits 8. 39999999

4. 13.00: Number of significant digits 4. 1300

5. 80,000,089: Number of significant digits 8. 80000089

6. 55430.00: Number of significant digits 7. 5543000

7. 0.000033: Number of significant digits 2. 33

8. 620.03080: Number of significant digits 8. 62003080

[tex]1. \hspace{3} 70000000000 = 7\times10^{10}\\2. \hspace{3} 0.000000048 = 4.8\times10 ^{-8}\\3. \hspace{3} 67890000 = 6.789\times10^7\\4. \hspace{3} 70500 = 7.05\times10^4\\5. \hspace{3} 450900800 = 4.509008\times10^8\\6. \hspace{3} 0.009045 = 9.045\times10^{-3}\\[/tex]