Question

name: dacian bect - 1 date: per: unit 1: the real numbers homework 7: scientific notation and comparing/ordering numbers this is a 2 - page document! directions: write each number in scientific notation. 1. 64,000 2. 0.0000049 3. 750 4. 0.00000000152 5. 82,300,000 6. 0.09 7. 52,640 8. 127.5 9. 2,320 10. the sun’s core temperature reaches close to 27,000,000 degrees fahrenheit. write this number in scientific notation. directions: write each number in standard form. 11. 5.3×10^4 12. 9.92×10^6 13. 4.1×10^(-2) 14. 2.726×10^8 15. 8.4×10^(-1) 16. 1.45×10^3 17. 9.392×10^(-4) 18. 6.02×10^2 19. 3.7528×10^5 20. the maximum upload size allowed for a file is 1.024×10^8 bytes. write this number in standard form. directions: place a < or > in the circle to complete each statement. 21. 3.05×10^4 〇 8.25×10^4 22. 5.729×10^3 〇 6.84×10^3 23. 2.5×10^(-2) 〇 7×10^(-3) 24. 6.27×10^(-7) 〇 1.8×10^(-5)

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 64000 to scientific notation

Move the decimal point 4 places to the left. So, $64000 = 6.4\times10^{4}$.

Step3: Convert 0.0000049 to scientific notation

Move the decimal point 6 places to the right. So, $0.0000049=4.9\times 10^{-6}$.

Step4: Convert 750 to scientific notation

Move the decimal point 2 places to the left. So, $750 = 7.5\times10^{2}$.

Step5: Convert 0.00000000152 to scientific notation

Move the decimal point 9 places to the right. So, $0.00000000152 = 1.52\times10^{-9}$.

Step6: Convert 82300000 to scientific notation

Move the decimal point 7 places to the left. So, $82300000=8.23\times 10^{7}$.

Step7: Convert 0.09 to scientific notation

Move the decimal point 2 places to the right. So, $0.09 = 9\times10^{-2}$.

Step8: Convert 52640 to scientific notation

Move the decimal point 4 places to the left. So, $52640 = 5.264\times10^{4}$.

Step9: Convert 127.5 to scientific notation

Move the decimal point 2 places to the left. So, $127.5 = 1.275\times10^{2}$.

Step10: Convert 2320 to scientific notation

Move the decimal point 3 places to the left. So, $2320 = 2.32\times10^{3}$.

Step11: Convert 27000000 to scientific notation

Move the decimal point 7 places to the left. So, $27000000=2.7\times 10^{7}$.

Step12: Recall standard - form rule

For $a\times10^{n}$, 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 $5.3\times10^{4}$ to standard form

Move the decimal point 4 places to the right. So, $5.3\times10^{4}=53000$.

Step14: Convert $9.92\times10^{6}$ to standard form

Move the decimal point 6 places to the right. So, $9.92\times10^{6}=9920000$.

Step15: Convert $4.1\times10^{-2}$ to standard form

Move the decimal point 2 places to the left. So, $4.1\times10^{-2}=0.041$.

Step16: Convert $2.726\times10^{8}$ to standard form

Move the decimal point 8 places to the right. So, $2.726\times10^{8}=272600000$.

Step17: Convert $8.4\times10^{-1}$ to standard form

Move the decimal point 1 place to the left. So, $8.4\times10^{-1}=0.84$.

Step18: Convert $1.45\times10^{3}$ to standard form

Move the decimal point 3 places to the right. So, $1.45\times10^{3}=1450$.

Step19: Convert $9.392\times10^{-4}$ to standard form

Move the decimal point 4 places to the left. So, $9.392\times10^{-4}=0.0009392$.

Step20: Convert $6.02\times10^{2}$ to standard form

Move the decimal point 2 places to the right. So, $6.02\times10^{2}=602$.

Step21: Convert $3.7528\times10^{6}$ to standard form

Move the decimal point 6 places to the right. So, $3.7528\times10^{6}=3752800$.

Step22: Convert $1.024\times10^{8}$ to standard form

Move the decimal point 8 places to the right. So, $1.024\times10^{8}=102400000$.

Step23: Compare $3.05\times10^{4}$ and $8.25\times10^{4}$

Since the exponents are the same, compare the coefficients. $3.05\lt8.25$, so $3.05\times10^{4}\lt8.25\times10^{4}$.

Step24: Compare $5.729\times10^{3}$ and $6.84\times10^{3}$

Since the exponents are the same, compare the coefficients. $5.729\lt6.84$, so $5.729\times10^{3}\lt6.84\times10^{3}$.

Step25: Compare $2.5\times10^{-2}$ and $7\times10^{-3}$

Rewrite $2.5\times10^{-2}$ as $25\times10^{-3}$. Since $25\gt7$, $2.5\times10^{-2}\gt7\times10^{-3}$.

Step26: Compare $6.27\times10^{-7}$ and $1.8\times10^{-5}$

Rewrite $6.27\times10^{-7}$ as $0.0627\times10^{-5}$. Since $0.0627\lt1.8$, $6.27\times10^{-7}\lt1.…

Answer:

1. $6.4\times10^{4}$
2. $4.9\times10^{-6}$
3. $7.5\times10^{2}$
4. $1.52\times10^{-9}$
5. $8.23\times10^{7}$
6. $9\times10^{-2}$
7. $5.264\times10^{4}$
8. $1.275\times10^{2}$
9. $2.32\times10^{3}$
10. $2.7\times10^{7}$
11. $53000$
12. $9920000$
13. $0.041$
14. $272600000$
15. $0.84$
16. $1450$
17. $0.0009392$
18. $602$
19. $3752800$
20. $102400000$
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