Sure! Let’s solve both sections of this worksheet step by step.
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##
✔ Part 1: Write the following scientific notation as ordinary numbers
Scientific notation is written as:
a × 10ⁿ, where 1 ≤ |a| < 10, and n is an integer.
To convert to an ordinary number:
- If
n is positive, move the decimal point
n places to the right.
- If
n is negative, move the decimal point
n places to the left.
---
(i) 4.32 × 10⁸
→ Move decimal 8 places to the right:
4.32 → 432,000,000
✔ Answer: 432,000,000
---
(ii) 1.05 × 10⁶
→ Move decimal 6 places to the right:
1.05 → 1,050,000
✔ Answer: 1,050,000
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(iii) 8.231 × 10¹⁰
→ Move decimal 10 places to the right:
8.231 → 82,310,000,000
✔ Answer: 82,310,000,000
*(Note: The original says “X” but it should be “×” — we assume it’s multiplication.)*
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(iv) 2.31 × 10⁻⁴
→ Move decimal 4 places to the left:
2.31 → 0.000231
✔ Answer: 0.000231
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(v) 7 × 10⁵
→ Move decimal 5 places to the right:
7 → 700,000
✔ Answer: 700,000
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##
✔ Part 2: Write the following numbers in scientific notation form
Rules for scientific notation:
- Move the decimal so that there's
only one non-zero digit to the left of the decimal.
- Count how many places you moved the decimal — that’s your exponent.
- If you moved the decimal
left, exponent is
positive.
- If you moved the decimal
right, exponent is
negative.
---
(i) 523,000
→ Move decimal 5 places to the left:
523,000 → 5.23 × 10⁵
✔ Answer: 5.23 × 10⁵
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(ii) 290,000,000
→ Move decimal 8 places to the left:
290,000,000 → 2.9 × 10⁸
✔ Answer: 2.9 × 10⁸
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(iii) 0.00056
→ Move decimal 4 places to the right:
0.00056 → 5.6 × 10⁻⁴
✔ Answer: 5.6 × 10⁻⁴
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(iv) 0.00008
→ Move decimal 5 places to the right:
0.00008 → 8 × 10⁻⁵
✔ Answer: 8 × 10⁻⁵
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(v) 0.000152
→ Move decimal 4 places to the right:
0.000152 → 1.52 × 10⁻⁴
✔ Answer: 1.52 × 10⁻⁴
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## 📝 Final Answers:
Part 1: Scientific Notation → Ordinary Numbers
(i) 432,000,000
(ii) 1,050,000
(iii) 82,310,000,000
(iv) 0.000231
(v) 700,000
Part 2: Ordinary Numbers → Scientific Notation
(i) 5.23 × 10⁵
(ii) 2.9 × 10⁸
(iii) 5.6 × 10⁻⁴
(iv) 8 × 10⁻⁵
(v) 1.52 × 10⁻⁴
Let me know if you’d like a printable version or explanation with diagrams! 😊
Parent Tip: Review the logic above to help your child master the concept of scientific notation worksheet.
