Question

grade 8 practice 8.ee.a.3: scientific notation
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name: tyreija hunt

1. write 75,800 in scientific notation.

a $0.758 \times 10^{5}$ b $75.8 \times 10^{3}$
c $7.58 \times 10^{4}$ d $758 \times 10^{2}$

1. write 2,220,000 in scientific notation.

a $222 \times 10^{4}$ b $0.222 \times 10^{7}$
c $2.22 \times 10^{6}$ d $22.2 \times 10^{5}$

1. write 713,000 in scientific notation.
2. write 92,800 in scientific notation.
3. write 5,640,000 in scientific notation.
4. write 0.0121 in scientific notation.

a $0.121 \times 10^{-3}$ b $121 \times 10^{-4}$
c $1.21 \times 10^{-2}$ d $0.121 \times 10^{-1}$

1. write 0.000346 in scientific notation.

a $0.346 \times 10^{-3}$ b $346 \times 10^{-6}$
c $3.46 \times 10^{-4}$ d $0.346 \times 10^{-4}$

1. write 0.0000281 in scientific notation.

a $2.81 \times 10^{-5}$ b $0.281 \times 10^{-4}$
c $0.281 \times 10^{-6}$ d $281 \times 10^{-7}$

1. write 0.000163 in scientific notation.
2. write 0.00000534 in scientific notation.
3. write 0.0000691 in scientific notation.
4. which number is not written in scientific notation?

a $6.7 \times 10^{2}$ b $5.5555 \times 10^{-24}$
c $3 \times 10^{-10}$ d $15.5 \times 10^{4}$
e $2.567 \times 10^{-2}$

Explanation:

Step1: Define scientific notation rule

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

Step2: Solve Q1: 75,800 to sci notation

Move decimal 4 left: $7.58 \times 10^4$

Step3: Solve Q2: 2,220,000 to sci notation

Move decimal 6 left: $2.22 \times 10^6$

Step4: Solve Q3: 713,000 to sci notation

Move decimal 5 left: $7.13 \times 10^5$

Step5: Solve Q4: 92,800 to sci notation

Move decimal 4 left: $9.28 \times 10^4$

Step6: Solve Q5: 5,640,000 to sci notation

Move decimal 6 left: $5.64 \times 10^6$

Step7: Solve Q6: 0.0121 to sci notation

Move decimal 2 right: $1.21 \times 10^{-2}$

Step8: Solve Q7: 0.000346 to sci notation

Move decimal 4 right: $3.46 \times 10^{-4}$

Step9: Solve Q8: 0.0000281 to sci notation

Move decimal 5 right: $2.81 \times 10^{-5}$

Step10: Solve Q9: 0.000163 to sci notation

Move decimal 4 right: $1.63 \times 10^{-4}$

Step11: Solve Q10: 0.00000534 to sci notation

Move decimal 6 right: $5.34 \times 10^{-6}$

Step12: Solve Q11: 0.0000691 to sci notation

Move decimal 5 right: $6.91 \times 10^{-5}$

Step13: Solve Q12: Identify invalid sci notation

Check which $a$ is not $1 \leq a <10$: $155 \times 10^4$ (155 ≥10)

Answer:

1. [C] $7.58 \times 10^4$
2. [C] $2.22 \times 10^6$
3. $7.13 \times 10^5$
4. $9.28 \times 10^4$
5. $5.64 \times 10^6$
6. [C] $1.21 \times 10^{-2}$
7. [C] $3.46 \times 10^{-4}$
8. [A] $2.81 \times 10^{-5}$
9. $1.63 \times 10^{-4}$
10. $5.34 \times 10^{-6}$
11. $6.91 \times 10^{-5}$
12. [D] $155 \times 10^4$