Absolutely! Let’s solve each conversion step by step, using the SI prefixes provided and converting to or from the base unit (meter, m). All answers will be given in
scientific notation as requested.
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SI Prefixes Recap (from worksheet):
- kilo = k = 10³
- centi = c = 10⁻²
- milli = m = 10⁻³
*(Note: The worksheet uses “m*” for milli — this is just a label; “m” alone is also used for meter, so we must be careful. In conversions, “mm” = millimeter = 10⁻³ m, “cm” = centimeter = 10⁻² m, “km” = kilometer = 10³ m.)*
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##
✔ Problem Solutions:
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1. Convert 4.0 cm to m.
- 1 cm = 10⁻² m
- So, 4.0 cm = 4.0 × 10⁻² m
✔ Answer: `4.0 × 10⁻² m`
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2. Convert 4.0 m to cm.
- 1 m = 100 cm = 10² cm
- So, 4.0 m = 4.0 × 10² cm
✔ Answer: `4.0 × 10² cm`
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3. Convert 40 mm to m.
- 1 mm = 10⁻³ m
- So, 40 mm = 40 × 10⁻³ m = 4.0 × 10¹ × 10⁻³ m = 4.0 × 10⁻² m
✔ Answer: `4.0 × 10⁻² m`
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4. Convert 40 m to mm.
- 1 m = 1000 mm = 10³ mm
- So, 40 m = 40 × 10³ mm = 4.0 × 10¹ × 10³ mm = 4.0 × 10⁴ mm
✔ Answer: `4.0 × 10⁴ mm`
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5. Convert 0.4 km to m.
- 1 km = 10³ m
- So, 0.4 km = 0.4 × 10³ m = 4.0 × 10⁻¹ × 10³ m = 4.0 × 10² m
✔ Answer: `4.0 × 10² m`
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6. Convert 0.4 m to km.
- 1 m = 10⁻³ km
- So, 0.4 m = 0.4 × 10⁻³ km = 4.0 × 10⁻¹ × 10⁻³ km = 4.0 × 10⁻⁴ km
✔ Answer: `4.0 × 10⁻⁴ km`
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7. Convert 40.0 m to mm.
- 1 m = 10³ mm
- So, 40.0 m = 40.0 × 10³ mm = 4.00 × 10¹ × 10³ mm = 4.00 × 10⁴ mm
✔ Answer: `4.00 × 10⁴ mm`
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8. Convert 400.0 m to mm.
- 1 m = 10³ mm
- So, 400.0 m = 400.0 × 10³ mm = 4.000 × 10² × 10³ mm = 4.000 × 10⁵ mm
✔ Answer: `4.000 × 10⁵ mm`
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## 📝 Summary of Answers (in scientific notation):
1. `4.0 × 10⁻² m`
2. `4.0 × 10² cm`
3. `4.0 × 10⁻² m`
4. `4.0 × 10⁴ mm`
5. `4.0 × 10² m`
6. `4.0 × 10⁻⁴ km`
7. `4.00 × 10⁴ mm`
8. `4.000 × 10⁵ mm`
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## 💡 Key Tips:
- When converting
to a smaller unit (e.g., m → mm), you
multiply → exponent increases.
- When converting
to a larger unit (e.g., cm → m), you
divide → exponent decreases.
- Always express final answer with correct significant figures and in scientific notation (one digit before decimal).
Let me know if you’d like to visualize these with a metric ladder or practice more!
Parent Tip: Review the logic above to help your child master the concept of si unit conversion worksheet.
