Question

1. 4.38×10^(-2) 11. 6.2×10^(-8) 12. 2×10^(-4) 13. 5,000 directions: write each number in scientific notation. 14. 7,400,000 15. 288 16. 0.00023 17. 0.97 18. 0.0000000894 19. the height of mount everest: 29,029 feet 20. the weight of a grain of sugar: 0.0000000625 21. 10^4 10^5 directions: place a <, > or = in the circle to complete each statement. 22. 10^(-2) 10^(-3)

Explanation:

1. $4.38\times10^{-2}=0.0438$
2. $6.2\times10^{-8}=0.000000062$
3. $2\times10^{-4}=0.0002$
4. $5000 = 5\times10^{3}$
5. $7400000=7.4\times10^{6}$
6. $288 = 2.88\times10^{2}$
7. $0.00023 = 2.3\times10^{-4}$
8. $0.97=9.7\times10^{-1}$
9. $0.0000000894 = 8.94\times10^{-8}$
10. The height of Mount Everest is $29029$ feet.
11. The weight of a grain of sugar is $0.0000000625=6.25\times10^{-8}$
12. Since $10^{4}=10000$ and $10^{5}=100000$, then $10^{4}<10^{5}$
13. Since $10^{-2}=\frac{1}{100}=0.01$ and $10^{-3}=\frac{1}{1000}=0.001$, then $10^{-2}>10^{-3}$

Step1: Convert scientific - notation to standard form

For numbers in scientific notation $a\times10^{n}$ ($1\leqslant|a|<10$), when $n>0$, move the decimal point $n$ places to the right; when $n < 0$, move the decimal point $|n|$ places to the left. For example, for $4.38\times10^{-2}$, move the decimal point 2 places to the left to get $0.0438$.

Step2: Convert standard - form to scientific notation

For a non - zero number $N$, express it as $a\times10^{n}$, where $1\leqslant|a|<10$. Move the decimal point to get $a$, and $n$ is the number of places the decimal point is moved. If the decimal point is moved to the left, $n>0$; if it is moved to the right, $n < 0$. For example, for $5000$, move the decimal point 3 places to the left to get $5\times10^{3}$.

Step3: Compare powers of 10

When comparing powers of 10 with the same base ($a = 10$ here), if $m>n$, then $10^{m}>10^{n}$ for positive exponents, and if $m < n$, then $10^{-m}>10^{-n}$ for negative exponents.

Answer:

1. $0.0438$
2. $0.000000062$
3. $0.0002$
4. $5\times10^{3}$
5. $7.4\times10^{6}$
6. $2.88\times10^{2}$
7. $2.3\times10^{-4}$
8. $9.7\times10^{-1}$
9. $8.94\times10^{-8}$
10. $29029$ feet
11. $6.25\times10^{-8}$
12. $<$
13. $>$