Question

1. $\frac{(1.8 \times 10^{5})}{(3 \times 10^{2})}$

$0.6 \times 10^{3}$
$6 \times 10^{2}$

1. $\frac{(3.6 \times 10^{8})}{(4 \times 10^{3})}$
2. $(9.8 \times 10^{7}) \times (8.2 \times 10^{4})$
3. $\frac{(1.44 \times 10^{9})}{(1.2 \times 10^{3})}$

write the following in scientific notation.

1. 0.0000000502
2. 432,000,000,000
3. 800,100,000,000,000

write the following in standard form.

1. $1.23 \times 10^{-5}$
2. $5 \times 10^{-3}$
3. 4.06e7

Explanation:

Step1: Divide coefficients, subtract exponents

$\frac{1.8}{3} \times 10^{5-2} = 0.6 \times 10^{3} = 6 \times 10^{2}$

Step2: Divide coefficients, subtract exponents

$\frac{3.6}{4} \times 10^{8-3} = 0.9 \times 10^{5} = 9 \times 10^{4}$

Step3: Multiply coefficients, add exponents

$9.8 \times 8.2 \times 10^{7+4} = 80.36 \times 10^{11} = 8.036 \times 10^{12}$

Step4: Divide coefficients, subtract exponents

$\frac{1.44}{1.2} \times 10^{9-3} = 1.2 \times 10^{6}$

Step5: Shift decimal to get scientific notation

$0.0000000502 = 5.02 \times 10^{-8}$

Step6: Shift decimal to get scientific notation

$432,000,000,000 = 4.32 \times 10^{11}$

Step7: Shift decimal to get scientific notation

$800,100,000,000,000 = 8.001 \times 10^{14}$

Step8: Shift decimal left for negative exponent

$1.23 \times 10^{-5} = 0.0000123$

Step9: Shift decimal left for negative exponent

$5 \times 10^{-3} = 0.005$

Step10: Convert E notation to standard form

$4.06\text{E}7 = 4.06 \times 10^{7} = 40600000$

Answer:

1. $6 \times 10^{2}$
2. $9 \times 10^{4}$
3. $8.036 \times 10^{12}$
4. $1.2 \times 10^{6}$
5. $5.02 \times 10^{-8}$
6. $4.32 \times 10^{11}$
7. $8.001 \times 10^{14}$
8. $0.0000123$
9. $0.005$
10. $40600000$