# Exercises: Scientific Notation (2.3)

## Exercises: Convert from Decimal Notation to Scientific Notation

Instructions: For questions 1–8, write each number in scientific notation.

1. $57\text{,}000$

2. $340\text{,}000$

Solution

$3.4\times {10}^{5}$

3. $8\text{,}750\text{,}000$

4. $1\text{,}290\text{,}000$

Solution

$1.29\times {10}^{6}$

5. $0.026$

6. $0.041$

Solution

$4.1\times {10}^{-2}$

7. $0.00000871$

8. $0.00000103$

Solution

$1.03\times {10}^{-6}$

## Exercises: Convert Scientific Notation to Decimal Form

Instructions: For questions 9–16, convert each number to decimal form.

9. $5.2\times {10}^{2}$

10. $8.3\times {10}^{2}$

Solution

$830$

11. $7.5\times {10}^{6}$

12. $1.6\times {10}^{10}$

Solution

$16\text{,}000\text{,}000\text{,}000$

13. $2.5\times {10}^{-2}$

14. $3.8\times {10}^{-2}$

Solution

$0.038$

15. $4.13\times {10}^{-5}$

16. $1.93\times {10}^{-5}$

Solution

$0.0000193$

## Exercises: Multiply and Divide Using Scientific Notation

17. $\left(3\times {10}^{-5}\right)\left(3\times {10}^{9}\right)$

18. $\left(2\times {10}^{2}\right)\left(1\times {10}^{-4}\right)$

Solution

$0.02$

19. $\left(7.1\times {10}^{-2}\right)\left(2.4\times {10}^{-4}\right)$

20. $\left(3.5\times {10}^{-4}\right)\left(1.6\times {10}^{-2}\right)$

Solution

$5.6\times {10}^{-6}$

## Exercises: Multiply and Divide Using Scientific Notation

21. $\frac{7\times {10}^{-3}}{1\times {10}^{-7}}$

22. $\frac{5\times {10}^{-2}}{1\times {10}^{-10}}$

Solution

$500\text{,}000\text{,}000$

23. $\frac{6\times {10}^{4}}{3\times {10}^{-2}}$

24. $\frac{8\times {10}^{6}}{4\times {10}^{-1}}$

Solution

$20\text{,}000\text{,}000$

## Exercises: Everyday Math

Instructions: For questions 25–36, answer the given everyday math word problem.

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

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

Solution

$6.85\times {10}^{9}$.

27. The average width of a human hair is $0.0018$ centimetres. Write the number in scientific notation.

28. The probability of winning the 2010 Megamillions lottery was about $0.0000000057$. Write the number in scientific notation.

Solution

$5.7\times {10}^{-9}$

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

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

Solution

$15\text{,}000\text{,}000\text{,}000\text{,}000$

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

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

Solution

$0.00001$

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

a. Write $4$ trillion in decimal notation.
b. Write $4$ trillion in scientific notation.

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

Solution

$1.545\times {10}^{8}$

35. Distance. The distance between Earth and one of the brightest stars in the night star is $33.7$ light years. One light year is about $6\text{,}000\text{,}000\text{,}000\text{,}000$ ($6$ 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 $18\text{,}600\text{,}000\text{,}000\text{,}000$ ($18.6$ trillion), according to the Federal Budget. The population of the United States was approximately $300\text{,}000\text{,}000$ 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. $1.86\times {10}^{13}$
b. $3\times {10}^{8}$
c. $6.2\times {10}^{4}$

## Exercises: Writing Exercises

Instructions: For question 37, answer the given writing exercise.

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