Question

name per:__ date:__ chemistry
people writing scientific notation practice & finding density activity
answer all the questions. see example below. show your work to get full credit.
examples: write the following numbers in scientific notation.

general form	234.576	0.0000030429	967.42	45.2×10³
scientific not.	2.34576×10²	3.0429×10⁻⁶	9.6742×10²	4.52×10⁴

write each number in scientific notation.

1. 0.0000002 2) 5400000
2. 120 4) 0.009
3. 6.7 6) 7660002
4. 9000000 8) 84×10³
5. 68900 10) 0.0000009

write each number in standard notation.

1. 0.9×10⁻¹ 12) 2×10⁻¹
2. 2×10³ 14) 804×10²
3. 2.66×10⁴ 16) 1.5×10⁻²
4. 7.75×10⁻¹ 18) 8.3×10⁷
5. 9.5×107 20) 1.71×107

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 $1.71\times10^{7}$)