Sure! Let’s solve each problem step by step and explain how to convert numbers to and from
scientific notation.
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## 🔢 PART 1: Write each number in scientific notation
Scientific notation format:
>
a × 10ⁿ, where
1 ≤ |a| < 10 and
n is an integer.
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1) 0.000055
- Move decimal point 5 places to the right to get 5.5 → exponent is
-5
-
✔ Answer: 5.5 × 10⁻⁵
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2) 225,000
- Move decimal point 5 places to the left to get 2.25 → exponent is
+5
-
✔ Answer: 2.25 × 10⁵
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3) 0.00179
- Move decimal 3 places right → 1.79 → exponent
-3
-
✔ Answer: 1.79 × 10⁻³
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4) 18,569
- Move decimal 4 places left → 1.8569 → exponent
+4
-
✔ Answer: 1.8569 × 10⁴
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5) 41,214
- Move decimal 4 places left → 4.1214 → exponent
+4
-
✔ Answer: 4.1214 × 10⁴
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6) 2,276
- Move decimal 3 places left → 2.276 → exponent
+3
-
✔ Answer: 2.276 × 10³
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7) 0.000207
- Move decimal 4 places right → 2.07 → exponent
-4
-
✔ Answer: 2.07 × 10⁻⁴
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8) 0.00939
- Move decimal 3 places right → 9.39 → exponent
-3
-
✔ Answer: 9.39 × 10⁻³
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9) 5.5 × 10⁵ — already in scientific notation!
- No change needed.
-
✔ Answer: 5.5 × 10⁵
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10) 8.2 × 10⁻⁴ — already in scientific notation!
- No change needed.
-
✔ Answer: 8.2 × 10⁻⁴
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## 📐 PART 2: Write each number in standard form
Standard form = regular number (not scientific notation)
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11) 1.0018 × 10¹¹
- Move decimal 11 places to the
right (since exponent is positive)
- Add zeros as needed: 100,180,000,000
-
✔ Answer: 100,180,000,000
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12) 7.754 × 10⁻⁴
- Move decimal 4 places to the
left (negative exponent)
- Result: 0.0007754
-
✔ Answer: 0.0007754
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13) 5.462 × 10⁴
- Move decimal 4 places right → 54,620
-
✔ Answer: 54,620
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14) 7.973 × 10²
- Move decimal 2 places right → 797.3
-
✔ Answer: 797.3
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15) 6.06 × 10⁶
- Move decimal 6 places right → 6,060,000
-
✔ Answer: 6,060,000
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16) 4.11 × 10³
- Move decimal 3 places right → 4,110
-
✔ Answer: 4,110
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17) 4.571 × 10⁴
- Move decimal 4 places right → 45,710
-
✔ Answer: 45,710
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18) 9.5 × 10⁵
- Move decimal 5 places right → 950,000
-
✔ Answer: 950,000
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19) 2.614 × 10⁶
- Move decimal 6 places right → 2,614,000
-
✔ Answer: 2,614,000
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20) 4 × 10⁻⁶
- Move decimal 6 places left → 0.000004
-
✔ Answer: 0.000004
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##
✔ Final Answers Summary:
Scientific Notation:
1) 5.5 × 10⁻⁵
2) 2.25 × 10⁵
3) 1.79 × 10⁻³
4) 1.8569 × 10⁴
5) 4.1214 × 10⁴
6) 2.276 × 10³
7) 2.07 × 10⁻⁴
8) 9.39 × 10⁻³
9) 5.5 × 10⁵
10) 8.2 × 10⁻⁴
Standard Form:
11) 100,180,000,000
12) 0.0007754
13) 54,620
14) 797.3
15) 6,060,000
16) 4,110
17) 45,710
18) 950,000
19) 2,614,000
20) 0.000004
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Let me know if you’d like a printable version or further explanations! 😊
Parent Tip: Review the logic above to help your child master the concept of scientific notation worksheet 8th grade.
