Question

kuta software - infinite algebra 1
name
writing in scientific notation
date
period
write each number in scientific notation.

1. 0.000006
2. 5400000
3. 60
4. 0.009
5. 6.7
6. 0.0000002
7. 2000000
8. 71×10³
9. 48900
10. 0.0000009
11. 0.63×10²
12. 33×10⁻³
13. 0.000216
14. 0.0042
15. 0.15×10⁻⁴
16. 4.8

Explanation:

Step1: Define scientific notation rule

Scientific notation is $a \times 10^n$, where $1 \leq a < 10$, $n$ is integer.

Step2: Convert 0.000006

Move decimal 6 right: $6 \times 10^{-6}$

Step3: Convert 5400000

Move decimal 6 left: $5.4 \times 10^{6}$

Step4: Convert 60

Move decimal 1 left: $6 \times 10^{1}$

Step5: Convert 0.009

Move decimal 3 right: $9 \times 10^{-3}$

Step6: Convert 6.7

Already valid: $6.7 \times 10^{0}$

Step7: Convert 0.0000002

Move decimal 7 right: $2 \times 10^{-7}$

Step8: Convert 2000000

Move decimal 6 left: $2 \times 10^{6}$

Step9: Convert $71 \times 10^3$

Adjust $a$ to 7.1, $n=4$: $7.1 \times 10^{4}$

Step10: Convert 48900

Move decimal 4 left: $4.89 \times 10^{4}$

Step11: Convert 0.0000009

Move decimal 7 right: $9 \times 10^{-7}$

Step12: Convert $0.63 \times 10^2$

Adjust $a$ to 6.3, $n=1$: $6.3 \times 10^{1}$

Step13: Convert $33 \times 10^{-3}$

Adjust $a$ to 3.3, $n=-2$: $3.3 \times 10^{-2}$

Step14: Convert 0.000216

Move decimal 4 right: $2.16 \times 10^{-4}$

Step15: Convert 0.0042

Move decimal 3 right: $4.2 \times 10^{-3}$

Step16: Convert $0.15 \times 10^{-2}$

Adjust $a$ to 1.5, $n=-3$: $1.5 \times 10^{-3}$

Step17: Convert 4.8

Already valid: $4.8 \times 10^{0}$

Answer:

1. $6 \times 10^{-6}$
2. $5.4 \times 10^{6}$
3. $6 \times 10^{1}$
4. $9 \times 10^{-3}$
5. $6.7 \times 10^{0}$
6. $2 \times 10^{-7}$
7. $2 \times 10^{6}$
8. $7.1 \times 10^{4}$
9. $4.89 \times 10^{4}$
10. $9 \times 10^{-7}$
11. $6.3 \times 10^{1}$
12. $3.3 \times 10^{-2}$
13. $2.16 \times 10^{-4}$
14. $4.2 \times 10^{-3}$
15. $1.5 \times 10^{-3}$
16. $4.8 \times 10^{0}$