Question

convert the following numbers into scientific notation:

1. 923
2. 0.00425
3. 4523000
4. 0.94300
5. 6750.
6. 92.03
7. 7.80
8. 0.00000032

convert the following numbers into standard notation:

1. 3.92400 x 10⁵
2. 9.2 x 10⁶
3. 4.391 x 10⁻³
4. 6.825 x 10⁻⁴
5. 4.6978 x 10⁴
6. 8.36 x 10¹
7. 2.46 x 10⁻⁵
8. 8.8 x 10²

Explanation:

Step1: Rewrite 923 to scientific form

$9.23 \times 10^{2}$

Step2: Rewrite 0.00425 to scientific form

$4.25 \times 10^{-3}$

Step3: Rewrite 4523000 to scientific form

$4.523 \times 10^{6}$

Step4: Rewrite 0.94300 to scientific form

$9.4300 \times 10^{-1}$

Step5: Rewrite 6750. to scientific form

$6.750 \times 10^{3}$

Step6: Rewrite 92.03 to scientific form

$9.203 \times 10^{1}$

Step7: Rewrite 7.80 to scientific form

$7.80 \times 10^{0}$

Step8: Rewrite 0.00000032 to scientific form

$3.2 \times 10^{-7}$

Step9: Convert $3.92400 \times 10^5$ to standard form

$3.92400 \times 100000 = 392400$

Step10: Convert $9.2 \times 10^6$ to standard form

$9.2 \times 1000000 = 9200000$

Step11: Convert $4.391 \times 10^{-3}$ to standard form

$4.391 \times \frac{1}{1000} = 0.004391$

Step12: Convert $6.825 \times 10^{-4}$ to standard form

$6.825 \times \frac{1}{10000} = 0.0006825$

Step13: Convert $4.6978 \times 10^4$ to standard form

$4.6978 \times 10000 = 46978$

Step14: Convert $8.36 \times 10^1$ to standard form

$8.36 \times 10 = 83.6$

Step15: Convert $2.46 \times 10^{-5}$ to standard form

$2.46 \times \frac{1}{100000} = 0.0000246$

Step16: Convert $8.8 \times 10^2$ to standard form

$8.8 \times 100 = 880$

Answer:

1. $9.23 \times 10^{2}$
2. $4.25 \times 10^{-3}$
3. $4.523 \times 10^{6}$
4. $9.4300 \times 10^{-1}$
5. $6.750 \times 10^{3}$
6. $9.203 \times 10^{1}$
7. $7.80 \times 10^{0}$
8. $3.2 \times 10^{-7}$
9. $392400$
10. $9200000$
11. $0.004391$
12. $0.0006825$
13. $46978$
14. $83.6$
15. $0.0000246$
16. $880$