name per:____ date:____ chemistry\npeople writing scientific notation practice & finding density…

name per:____ date:____ chemistry\npeople writing scientific notation practice & finding density activity\nanswer all the questions. see example below. show your work to get full credit.\nexamples: write the following numbers in scientific notation.\n|general form|234.576|0.0000030429|967.42|45.2×10³|\n|scientific not.|2.34576×10²|3.0429×10⁻⁶|9.6742×10²|4.52×10⁴|\nwrite each number in scientific notation.\n1) 0.0000002 2) 5400000\n3) 120 4) 0.009\n5) 6.7 6) 7660002\n7) 9000000 8) 84×10³\n9) 68900 10) 0.0000009\nwrite each number in standard notation.\n11) 0.9×10⁻¹ 12) 2×10⁻¹\n13) 2×10³ 14) 804×10²\n15) 2.66×10⁴ 16) 1.5×10⁻²\n17) 7.75×10⁻¹ 18) 8.3×10⁷\n19) 9.5×107 20) 1.71×107

name per:____ date:____ chemistry\npeople writing scientific notation practice & finding density activity\nanswer all the questions. see example below. show your work to get full credit.\nexamples: write the following numbers in scientific notation.\n|general form|234.576|0.0000030429|967.42|45.2×10³|\n|scientific not.|2.34576×10²|3.0429×10⁻⁶|9.6742×10²|4.52×10⁴|\nwrite each number in scientific notation.\n1) 0.0000002 2) 5400000\n3) 120 4) 0.009\n5) 6.7 6) 7660002\n7) 9000000 8) 84×10³\n9) 68900 10) 0.0000009\nwrite each number in standard notation.\n11) 0.9×10⁻¹ 12) 2×10⁻¹\n13) 2×10³ 14) 804×10²\n15) 2.66×10⁴ 16) 1.5×10⁻²\n17) 7.75×10⁻¹ 18) 8.3×10⁷\n19) 9.5×107 20) 1.71×107

Answer

Explanation:

Step1: Recall scientific - notation rule

Scientific notation is of the form $a\times10^{n}$, where $1\leq|a|\lt10$ and $n$ is an integer.

Step2: Convert 0.0000002 to scientific notation

Move the decimal point 7 places to the right to get $a = 2$. Since we moved the decimal point 7 places to the right, $n=-7$. So, $0.0000002 = 2\times10^{-7}$.

Step3: Convert 5400000 to scientific notation

Move the decimal point 6 places to the left to get $a = 5.4$. Since we moved the decimal point 6 places to the left, $n = 6$. So, $5400000=5.4\times10^{6}$.

Step4: Convert 120 to scientific notation

Move the decimal point 2 places to the left to get $a = 1.2$. Since we moved the decimal point 2 places to the left, $n = 2$. So, $120 = 1.2\times10^{2}$.

Step5: Convert 0.009 to scientific notation

Move the decimal point 3 places to the right to get $a = 9$. Since we moved the decimal point 3 places to the right, $n=-3$. So, $0.009=9\times10^{-3}$.

Step6: Convert 6.7 to scientific notation

$6.7$ is already in the form $a\times10^{n}$ with $a = 6.7$ and $n = 0$. So, $6.7=6.7\times10^{0}$.

Step7: Convert 7660002 to scientific notation

Move the decimal point 6 places to the left to get $a = 7.660002$. Since we moved the decimal point 6 places to the left, $n = 6$. So, $7660002=7.660002\times10^{6}$.

Step8: Convert 9000000 to scientific notation

Move the decimal point 6 places to the left to get $a = 9$. Since we moved the decimal point 6 places to the left, $n = 6$. So, $9000000=9\times10^{6}$.

Step9: Convert $84\times10^{3}$ to scientific notation

First, $84\times10^{3}=84000$. Then move the decimal point 4 places to the left to get $a = 8.4$. Since we moved the decimal point 4 places to the left, $n = 4$. So, $84\times10^{3}=8.4\times10^{4}$.

Step10: Convert 68900 to scientific notation

Move the decimal point 4 places to the left to get $a = 6.89$. Since we moved the decimal point 4 places to the left, $n = 4$. So, $68900=6.89\times10^{4}$.

Step11: Convert 0.0000009 to scientific notation

Move the decimal point 7 places to the right to get $a = 9$. Since we moved the decimal point 7 places to the right, $n=-7$. So, $0.0000009=9\times10^{-7}$.

Step12: Recall standard - notation rule

To convert from scientific notation $a\times10^{n}$ to standard notation, if $n\gt0$, move the decimal point $n$ places to the right; if $n\lt0$, move the decimal point $|n|$ places to the left.

Step13: Convert $0.9\times10^{-1}$ to standard notation

Since $n=-1$, move the decimal point 1 place to the left. So, $0.9\times10^{-1}=0.09$.

Step14: Convert $2\times10^{-1}$ to standard notation

Since $n=-1$, move the decimal point 1 place to the left. So, $2\times10^{-1}=0.2$.

Step15: Convert $2\times10^{5}$ to standard notation

Since $n = 5$, move the decimal point 5 places to the right. So, $2\times10^{5}=200000$.

Step16: Convert $804\times10^{2}$ to standard notation

First, $804\times10^{2}=80400$.

Step17: Convert $2.66\times10^{4}$ to standard notation

Since $n = 4$, move the decimal point 4 places to the right. So, $2.66\times10^{4}=26600$.

Step18: Convert $1.5\times10^{-2}$ to standard notation

Since $n=-2$, move the decimal point 2 places to the left. So, $1.5\times10^{-2}=0.015$.

Step19: Convert $7.75\times10^{-1}$ to standard notation

Since $n=-1$, move the decimal point 1 place to the left. So, $7.75\times10^{-1}=0.775$.

Step20: Convert $8.3\times10^{7}$ to standard notation

Since $n = 7$, move the decimal point 7 places to the right. So, $8.3\times10^{7}=83000000$.

Step21: Convert $9.5\times107$ (assuming it's $9.5\times10^{7}$) to standard notation

Since $n = 7$, move the decimal point 7 places to the right. So, $9.5\times10^{7}=95000000$.

Step22: Convert $1.71\times107$ (assuming it's $1.71\times10^{7}$) to standard notation

Since $n = 7$, move the decimal point 7 places to the right. So, $1.71\times10^{7}=17100000$.

Answer:

  1. $2\times10^{-7}$
  2. $5.4\times10^{6}$
  3. $1.2\times10^{2}$
  4. $9\times10^{-3}$
  5. $6.7\times10^{0}$
  6. $7.660002\times10^{6}$
  7. $9\times10^{6}$
  8. $8.4\times10^{4}$
  9. $6.89\times10^{4}$
  10. $9\times10^{-7}$
  11. $0.09$
  12. $0.2$
  13. $200000$
  14. $80400$
  15. $26600$
  16. $0.015$
  17. $0.775$
  18. $83000000$
  19. $95000000$ (assuming $9.5\times10^{7}$)
  20. $17100000$ (assuming $1.71\times10^{7}$)