Sure! Let’s solve each problem step by step and explain how to convert between
standard form and
scientific notation.
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## 🔢 Part 1: Write the following in scientific notation
Scientific notation format:
>
a × 10ⁿ, where
1 ≤ |a| < 10 and
n is an integer.
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1. 384.32
- Move the decimal point so that there's only one non-zero digit to the left.
- 384.32 → move decimal 2 places left →
3.8432
- Since we moved 2 places left, exponent is
+2
✔ Answer: 3.8432 × 10²
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2. 87521
- Move decimal 4 places left →
8.7521
- Exponent = +4
✔ Answer: 8.7521 × 10⁴
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3. 3910.28 × 10⁴
This is
not in proper scientific notation because 3910.28 is not between 1 and 10.
- First, write 3910.28 in scientific notation:
→ 3910.28 = 3.91028 × 10³
- Now multiply by 10⁴:
→ (3.91028 × 10³) × 10⁴ =
3.91028 × 10⁷
✔ Answer: 3.91028 × 10⁷
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4. 0.001247
- Move decimal 3 places right →
1.247
- Since we moved right, exponent is
–3
✔ Answer: 1.247 × 10⁻³
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## 📐 Part 2: Write the following in standard form
Standard form = regular number (no exponents)
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5. 3.23 × 10⁻⁶
- Negative exponent → move decimal 6 places
left
- 3.23 → move decimal 6 places left:
→ 0.00000323
✔ Answer: 0.00000323
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6. 1.589 × 10⁴
- Positive exponent → move decimal 4 places
right
- 1.589 → 15890.
✔ Answer: 15890
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7. 8.29 × 10¹
- Move decimal 1 place right → 82.9
✔ Answer: 82.9
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8. 6.75 × 10⁻³
- Move decimal 3 places left → 0.00675
✔ Answer: 0.00675
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##
✔ Final Answers:
Scientific Notation:
1. 384.32 =
3.8432 × 10²
2. 87521 =
8.7521 × 10⁴
3. 3910.28 × 10⁴ =
3.91028 × 10⁷
4. 0.001247 =
1.247 × 10⁻³
Standard Form:
5. 3.23 × 10⁻⁶ =
0.00000323
6. 1.589 × 10⁴ =
15890
7. 8.29 × 10¹ =
82.9
8. 6.75 × 10⁻³ =
0.00675
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Let me know if you’d like a printable version or further explanation on any step! 😊
Parent Tip: Review the logic above to help your child master the concept of scientific notation problems worksheet.
