section_reviews_(all)_holt_physics.pdf - Free Printable

Problem Analysis:

The task involves solving problems related to scientific notation, prefixes, and significant figures. Let's break down each question step by step.

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Question 1: How many picometers are there in 1 mm?

#### Solution:
1. Understand the prefixes:
- \(1 \text{ mm} = 10^{-3} \text{ m}\) (milli- prefix)
- \(1 \text{ pm} = 10^{-12} \text{ m}\) (pico- prefix)

2. Convert millimeters to meters:
\[
1 \text{ mm} = 10^{-3} \text{ m}
\]

3. Convert meters to picometers:
\[
1 \text{ m} = 10^{12} \text{ pm}
\]
Therefore,
\[
10^{-3} \text{ m} = 10^{-3} \times 10^{12} \text{ pm} = 10^9 \text{ pm}
\]

4. Final Answer:
\[
\boxed{10^9}
\]

---

Question 2: How many micrometers are there in 1 kg?

#### Solution:
1. Understand the units:
- \(1 \text{ kg}\) is a unit of mass.
- \(1 \mu\text{m}\) is a unit of length.

2. Analysis:
- The question asks for a conversion between mass (kg) and length (\(\mu\text{m}\)), which is not possible because they are different physical quantities. There is no direct relationship or conversion factor between mass and length.

3. Final Answer:
\[
\boxed{\text{Not possible}}
\]

---

Question 3: How many nanometers are there in 1 cm?

#### Solution:
1. Understand the prefixes:
- \(1 \text{ cm} = 10^{-2} \text{ m}\) (centi- prefix)
- \(1 \text{ nm} = 10^{-9} \text{ m}\) (nano- prefix)

2. Convert centimeters to meters:
\[
1 \text{ cm} = 10^{-2} \text{ m}
\]

3. Convert meters to nanometers:
\[
1 \text{ m} = 10^9 \text{ nm}
\]
Therefore,
\[
10^{-2} \text{ m} = 10^{-2} \times 10^9 \text{ nm} = 10^7 \text{ nm}
\]

4. Final Answer:
\[
\boxed{10^7}
\]

---

Question 4: Rewrite the following quantities in scientific notation without prefixes.

#### Part (a): 5.02 gigayards
1. Understand the prefix:
- \(1 \text{ G} = 10^9\)

2. Rewrite:
\[
5.02 \text{ gigayards} = 5.02 \times 10^9 \text{ yards}
\]

#### Part (b): 0.000021 milliseconds
1. Understand the prefix:
- \(1 \text{ ms} = 10^{-3} \text{ s}\)

2. Rewrite:
\[
0.000021 \text{ ms} = 0.000021 \times 10^{-3} \text{ s} = 2.1 \times 10^{-8} \text{ s}
\]

#### Part (c): 5637 nanoseconds
1. Understand the prefix:
- \(1 \text{ ns} = 10^{-9} \text{ s}\)

2. Rewrite:
\[
5637 \text{ ns} = 5637 \times 10^{-9} \text{ s} = 5.637 \times 10^{-6} \text{ s}
\]

#### Part (d): 0.000000000001 megapascals
1. Understand the prefix:
- \(1 \text{ MPa} = 10^6 \text{ Pa}\)

2. Rewrite:
\[
0.000000000001 \text{ MPa} = 0.000000000001 \times 10^6 \text{ Pa} = 1 \times 10^{-6} \text{ Pa}
\]

#### Final Answers:
\[
\boxed{5.02 \times 10^9, 2.1 \times 10^{-8}, 5.637 \times 10^{-6}, 1 \times 10^{-6}}
\]

---

Question 5: Rewrite the following quantities to units with SI prefixes.

#### Part (a): 583472 g
1. Understand the SI prefixes:
- \(1 \text{ kg} = 10^3 \text{ g}\)

2. Convert grams to kilograms:
\[
583472 \text{ g} = \frac{583472}{10^3} \text{ kg} = 583.472 \text{ kg}
\]

#### Part (b): 0.000000032 m
1. Understand the SI prefixes:
- \(1 \text{ nm} = 10^{-9} \text{ m}\)

2. Convert meters to nanometers:
\[
0.000000032 \text{ m} = 0.000000032 \times 10^9 \text{ nm} = 32 \text{ nm}
\]

#### Part (c): 53236 V
1. Understand the SI prefixes:
- \(1 \text{ kV} = 10^3 \text{ V}\)

2. Convert volts to kilovolts:
\[
53236 \text{ V} = \frac{53236}{10^3} \text{ kV} = 53.236 \text{ kV}
\]

#### Part (d): 421 × 10⁻⁹ F
1. Understand the SI prefixes:
- \(1 \text{ nF} = 10^{-9} \text{ F}\)

2. Convert farads to nanofarads:
\[
421 \times 10^{-9} \text{ F} = 421 \text{ nF}
\]

#### Final Answers:
\[
\boxed{583.472 \text{ kg}, 32 \text{ nm}, 53.236 \text{ kV}, 421 \text{ nF}}
\]

---

Question 6: Express the measurement 4.28478164 g with 8, 6, and 4 significant figures.

#### Solution:
1. Original value:
\[
4.28478164 \text{ g}
\]

2. Round to 8 significant figures:
- The original value already has 10 significant figures. To round to 8, we keep the first 8 digits and round the 9th digit.
\[
4.2847816 \text{ g}
\]

3. Round to 6 significant figures:
- Keep the first 6 digits and round the 7th digit.
\[
4.28478 \text{ g}
\]

4. Round to 4 significant figures:
- Keep the first 4 digits and round the 5th digit.
\[
4.285 \text{ g}
\]

#### Final Answers:
\[
\boxed{4.2847816, 4.28478, 4.285}
\]

---

Final Summary of All Answers:

1. \(\boxed{10^9}\)
2. \(\boxed{\text{Not possible}}\)
3. \(\boxed{10^7}\)
4. \(\boxed{5.02 \times 10^9, 2.1 \times 10^{-8}, 5.637 \times 10^{-6}, 1 \times 10^{-6}}\)
5. \(\boxed{583.472 \text{ kg}, 32 \text{ nm}, 53.236 \text{ kV}, 421 \text{ nF}}\)
6. \(\boxed{4.2847816, 4.28478, 4.285}\)