Practice with Integer Exponents and Scientific Notation

Convert from Decimal Notation to Scientific Notation
In the following exercises, write each number in scientific notation.

1. \(280,000\)
   
   
2. \(1,290,000\)
   
   
3. \(0.041\)
   
   
4. \(0.0000103\)
   
   
5. The population of the world on July 4, 2010 was more than \(6,850,000,000\).
   
   
6. The probability of winning the 2010 Megamillions lottery is about \(0.0000000057\).

Convert Scientific Notation to Decimal Form
In the following exercises, convert each number to decimal form.

7. \(8.3 \times 10^2\)
   
   
8. \(1.6 \times 10^{10}\)
   
   
9. \(2.8 \times 10^{−2}\)
   
   
10. \(6.15 \times 10^{−8}\)
    
    
11. At the start of 2012, the US federal budget had a deficit of more than \($1.5 \times 10^{13}\).
    
    
12. The width of a proton is \(1 \times 10^{−5}\) of the width of an atom.

Multiply and Divide Using Scientific Notation
In the following exercises, multiply or divide and write your answer in decimal form.

13. \((3 \times 10^2)(1 \times 10^{−5})\)
    
    
14. \((2.1 \times 10^{−4})(3.5 \times 10^{−2})\)
    
    
15. \(\frac{8 \times10^6}{4 \times 10^{−1}}\)
    
    
16. \(\frac{5 \times 10^{−3}}{1 \times 10^{−10}}\)

Source: Rice University, https://openstax.org/books/prealgebra-2e/pages/10-5-integer-exponents-and-scientific-notation
This work is licensed under a Creative Commons Attribution 4.0 License.

1. \(2.8 × 10^5\)
   
   
2. \(1.29 × 10^6\)
   
   
3. \(4.1 × 10^{−2}\)
   
   
4. \(1.03 × 10^{−5}\)
   
   
5. \(6.85 × 10^9\)
   
   
6. \(5.7 × 10^{−9}\)
   
   
7. \(830\)
   
   
8. \(16,000,000,000\)
   
   
9. \(0.028\)
   
   
10. \(0.0000000615\)
    
    
11. \($15,000,000,000,000\)
    
    
12. \(0.00001\)
    
    
13. \(0.003\)
    
    
14. \(0.00000735\)
    
    
15. \(20,000,000\)
    
    
16. \(50,000,000\)