Question

homework: ch. 8.6 scientific notation name elope h date pd scientific notation three students practiced converting values into scientific notation as shown. in 1 - 3, describe the mistake each student made and correct their work. isla: 12,560,000 ↓ 12.56 × 10⁶ lenny: 0.0000383 ↓ 3.83 × 10⁵ jamie: 7,770,000,000 ↓ 7.77 × 10⁷ 1. describe isla’s mistake: correct isla’s work: 2. describe lenny’s mistake: correct lenny’s work: 3. describe jamie’s mistake: correct jamie’s work: in 4 - 6, convert each scientific notation value into standard notation. 4. 5.5 × 10⁻⁸ 5. 1.625 × 10⁷ 6. 3 × 10⁻⁴ 7. gabi is converting 0.000098 into scientific notation as shown below. which correctly represents the missing power of 10? 9.8 × 10⁷ a. 5 b. -5 c. 6 d. -6 8. asher is involved in a competition where the grand prize is $150,000 dollars. represent the amount of the grand prize in scientific notation. 9. mrs. ferreria asked her students to write a number in scientific notation that is greater than 500 but less than 5,000. circle the name of any student who correctly completed the task. justice: 5.25 × 10³ plaire: 6.1 × 10³ denzel: 5.78 × 10² piper: 3.5 × 10³

Explanation:

Step1: Analyze Isla's error

Scientific notation requires a coefficient where $1 \leq |a| < 10$. Isla used 12.56, which is outside this range. To fix, adjust coefficient and exponent:
$12.56 \times 10^6 = 1.256 \times 10^7$

Step2: Analyze Lenny's error

Lenny used a positive exponent for a number less than 1. For small decimals, the exponent must be negative. Count decimal shifts: move 5 places right to get 3.83, so exponent is $-5$:
$3.83 \times 10^{-5}$

Step3: Analyze Jamie's error

Jamie counted the exponent incorrectly. For 7,770,000,000, move the decimal 9 places left to get 7.77, so exponent is 9:
$7.77 \times 10^9$

Step4: Convert $5.5 \times 10^{-8}$ to standard

Negative exponent: move decimal 8 places left:
$0.00000005.5 = 0.000000055$

Step5: Convert $1.625 \times 10^7$ to standard

Positive exponent: move decimal 7 places right:
$1.6250000 = 16250000$

Step6: Convert $3 \times 10^{-4}$ to standard

Negative exponent: move decimal 4 places left:
$0.0003$

Step7: Solve Gabi's missing exponent

0.000098 needs decimal moved 5 places right to get 9.8, so exponent is $-5$:
Select option b

Step8: Convert $150,000$ to scientific notation

Move decimal 5 places left to get 1.5, exponent is 5:
$1.5 \times 10^5$

Step9: Evaluate students' 500-5000 range

• $5.25 \times 10^3 = 5250$ (too big)
• $6.1 \times 10^3 = 6100$ (too big)
• $5.78 \times 10^2 = 578$ (in range)
• $3.5 \times 10^3 = 3500$ (in range)

Circle Denzel and Piper

Answer:

1. Describe Isla's mistake: Coefficient not between 1-10

Correct Isla's work: $1.256 \times 10^7$

1. Describe Lenny's mistake: Wrong exponent sign

Correct Lenny's work: $3.83 \times 10^{-5}$

1. Describe Jamie's mistake: Incorrect exponent count

Correct Jamie's work: $7.77 \times 10^9$

1. $0.000000055$
2. $16250000$
3. $0.0003$
4. b. -5
5. $1.5 \times 10^5$
6. Denzel, Piper