Let's solve this step-by-step.
This is a
maze-style puzzle where you:
1. Start at the center diamond labeled
"START" with the number:
3.205 × 10⁷
2. Convert that number to
standard form, then follow the arrow labeled with that value to the next box.
3. Repeat the process: convert the scientific notation in each box to standard form, and follow the arrow with the matching number.
4. Continue until you reach the
END.
---
Step 1: Start at 3.205 × 10⁷
Convert to standard form:
- Move the decimal 7 places to the right:
3.205 → 32,050,000
So, we look for the arrow labeled
32,050,000.
From the START box, there are two arrows:
- One labeled
32,050,000 → points to
7.4 × 10⁵
- Another labeled
32,050,000,000 → too big (that’s 3.205 × 10⁹)
✔ So, follow
32,050,000 → leads to
7.4 × 10⁵
---
Step 2: Convert 7.4 × 10⁵
Move decimal 5 places right:
- 7.4 → 740,000
Look for arrow labeled
740,000
From
7.4 × 10⁵, the arrow labeled
740,000 goes to
9.99 × 10⁻⁶
✔ Next box:
9.99 × 10⁻⁶
---
Step 3: Convert 9.99 × 10⁻⁶
Negative exponent → move decimal 6 places to the left:
- 9.99 → 0.00000999
Look for arrow labeled
0.00000999
From
9.99 × 10⁻⁶, the arrow labeled
0.00000999 goes to
5.603 × 10³
✔ Next box:
5.603 × 10³
---
Step 4: Convert 5.603 × 10³
Move decimal 3 places right:
- 5.603 → 5,603
Look for arrow labeled
5,603
From
5.603 × 10³, the arrow labeled
5,603 goes to
9.0909 × 10²
✔ Next box:
9.0909 × 10²
---
Step 5: Convert 9.0909 × 10²
Move decimal 2 places right:
- 9.0909 → 909.09
Look for arrow labeled
909.09
From
9.0909 × 10², the arrow labeled
909.09 goes to
9.9 × 10⁰
✔ Next box:
9.9 × 10⁰
---
Step 6: Convert 9.9 × 10⁰
Any number × 10⁰ = itself
- 9.9 × 1 =
9.9
Look for arrow labeled
9.9
From
9.9 × 10⁰, the arrow labeled
9.9 goes to
1.0 × 10⁰
✔ Next box:
1.0 × 10⁰
---
Step 7: Convert 1.0 × 10⁰
=
1.0
Look for arrow labeled
1
From
1.0 × 10⁰, the arrow labeled
1 goes to
END
✔ We've reached the
END!
---
✔ Final Answer Path:
START →
3.205 × 10⁷ →
32,050,000 →
7.4 × 10⁵ →
740,000 →
9.99 × 10⁻⁶ →
0.00000999 →
5.603 × 10³ →
5,603 →
9.0909 × 10² →
909.09 →
9.9 × 10⁰ →
9.9 →
1.0 × 10⁰ →
1 →
END
---
🟩 Solution Summary:
You begin at
3.205 × 10⁷, convert it to
32,050,000, and follow the path through the maze by converting each scientific notation number to standard form and following the corresponding arrow. The correct sequence leads you directly to the
END without any dead ends.
✔ Answer: The correct path from
START to
END is:
> 3.205 × 10⁷ → 7.4 × 10⁵ → 9.99 × 10⁻⁶ → 5.603 × 10³ → 9.0909 × 10² → 9.9 × 10⁰ → 1.0 × 10⁰ → END
This is a fun way to practice
scientific notation conversions!
Parent Tip: Review the logic above to help your child master the concept of scientific notation coloring worksheet.
