# Exercises: Scientific Notation (2.3)

**Exercises: Convert from Decimal Notation to Scientific Notation**

**1. [latex]57\text{,}000[/latex]**

**2. [latex]340\text{,}000[/latex]**

**Solution**

[latex]3.4\times {10}^{5}[/latex]

**3. [latex]8\text{,}750\text{,}000[/latex]**

**4. [latex]1\text{,}290\text{,}000[/latex]**

**Solution**

[latex]1.29\times {10}^{6}[/latex]

**5. [latex]0.026[/latex]**

**6. [latex]0.041[/latex]**

**Solution**

[latex]4.1\times {10}^{-2}[/latex]

**7. [latex]0.00000871[/latex]**

**8. [latex]0.00000103[/latex]**

**Solution**

[latex]1.03\times {10}^{-6}[/latex]

**Exercises: Convert Scientific Notation to Decimal Form**

**9. [latex]5.2\times {10}^{2}[/latex]**

**10. [latex]8.3\times {10}^{2}[/latex]**

**Solution**

[latex]830[/latex]

**11. [latex]7.5\times {10}^{6}[/latex]**

**12. [latex]1.6\times {10}^{10}[/latex]**

**Solution**

[latex]16\text{,}000\text{,}000\text{,}000[/latex]

**13. [latex]2.5\times {10}^{-2}[/latex]**

**14. [latex]3.8\times {10}^{-2}[/latex]**

**Solution**

[latex]0.038[/latex]

**15. [latex]4.13\times {10}^{-5}[/latex]**

**16. [latex]1.93\times {10}^{-5}[/latex]**

**Solution**

[latex]0.0000193[/latex]

**Exercises: Multiply and Divide Using Scientific Notation**

**17. [latex]\left(3\times {10}^{-5}\right)\left(3\times {10}^{9}\right)[/latex]**

**18. [latex]\left(2\times {10}^{2}\right)\left(1\times {10}^{-4}\right)[/latex]**

**Solution**

[latex]0.02[/latex]

**19. [latex]\left(7.1\times {10}^{-2}\right)\left(2.4\times {10}^{-4}\right)[/latex]**

**20. [latex]\left(3.5\times {10}^{-4}\right)\left(1.6\times {10}^{-2}\right)[/latex]**

**Solution**

[latex]5.6\times {10}^{-6}[/latex]

**Exercises: Multiply and Divide Using Scientific Notation**

**21. [latex]\frac{7\times {10}^{-3}}{1\times {10}^{-7}}[/latex]**

**22. [latex]\frac{5\times {10}^{-2}}{1\times {10}^{-10}}[/latex]**

**Solution**

[latex]500\text{,}000\text{,}000[/latex]

**23. [latex]\frac{6\times {10}^{4}}{3\times {10}^{-2}}[/latex]****24. [latex]\frac{8\times {10}^{6}}{4\times {10}^{-1}}[/latex]**

**Solution**

[latex]20\text{,}000\text{,}000[/latex]

**Exercises: Everyday Math**

**25. The population of the United States on July 4, 2010 was almost [latex]310\text{,}000\text{,}000[/latex]. Write the number in scientific notation.**

**26. The population of the world on July 4, 2010 was more than [latex]6\text{,}850\text{,}000\text{,}000[/latex]. Write the number in scientific notation**

**Solution**

[latex]6.85\times {10}^{9}[/latex].

**27. The average width of a human hair is [latex]0.0018[/latex] centimetres. Write the number in scientific notation.**

**28. The probability of winning the 2010 Megamillions lottery was about [latex]0.0000000057[/latex]. Write the number in scientific notation.**

**Solution**

[latex]5.7\times {10}^{-9}[/latex]

**29. In 2010, the number of Facebook users each day who changed their status to ‘engaged’ was [latex]2\times {10}^{4}[/latex]. Convert this number to decimal form.**

**30. At the start of 2012, the US federal budget had a deficit of more than [latex]$1.5\times {10}^{13}[/latex]. Convert this number to decimal form.**

**Solution**

[latex]15\text{,}000\text{,}000\text{,}000\text{,}000[/latex]

**31. The concentration of carbon dioxide in the atmosphere is [latex]3.9\times {10}^{-4}[/latex]. Convert this number to decimal form.**

**32. The width of a proton is [latex]1\times {10}^{-5}[/latex] of the width of an atom. Convert this number to decimal form.**

**Solution**

[latex]0.00001[/latex]

**33. Health care costs.** The Centres for Medicare and Medicaid projects that consumers will spend more than [latex]$4[/latex] trillion on health care by 2017.

**a. Write [latex]4[/latex] trillion in decimal notation.**

**b. Write [latex]4[/latex] trillion in scientific notation.**

**34. Coin production.** In 1942, the U.S. Mint produced [latex]154\text{,}500\text{,}000[/latex] nickels. Write [latex]154\text{,}500\text{,}000[/latex] in scientific notation.

**Solution**

[latex]1.545\times {10}^{8}[/latex]

**35. Distance.** The distance between Earth and one of the brightest stars in the night star is [latex]33.7[/latex] light years. One light year is about [latex]6\text{,}000\text{,}000\text{,}000\text{,}000[/latex] ([latex]6[/latex] trillion), miles.

**a. Write the number of miles in one light year in scientific notation.**

**b. Use scientific notation to find the distance between Earth and the star in miles. Write the answer in scientific notation.**

**36. Debt.** At the end of fiscal year 2015 the gross United States federal government debt was estimated to be approximately [latex]$18\text{,}600\text{,}000\text{,}000\text{,}000[/latex] ([latex]$18.6[/latex] trillion), according to the Federal Budget. The population of the United States was approximately [latex]300\text{,}000\text{,}000[/latex] people at the end of fiscal year 2015.

**a. Write the debt in scientific notation.**

**b. Write the population in scientific notation.**

**c. Find the amount of debt per person by using scientific notation to divide the debt by the population. Write the answer in scientific notation.**

**Solution**

a. [latex]1.86\times {10}^{13}[/latex]

b. [latex]3\times {10}^{8}[/latex]

c. [latex]6.2\times {10}^{4}[/latex]

**Exercises: Writing Exercises**

**37. When you convert a number from decimal notation to scientific notation, how do you know if the exponent will be positive or negative?**

**Solution**

Answers will vary