https://file.aiquickdraw.com/mathbot/file/1727047876367sg1iru7z.jpg

Let's go through each of the questions in the image and solve them step by step.

### 1. \( 0.02 \, \text{jam} + 20 \, \text{menit} = \, \, \text{detik} \)

- 1 hour = 3600 seconds, so:
  - \( 0.02 \, \text{jam} = 0.02 \times 3600 = 72 \, \text{detik} \)
- 1 minute = 60 seconds, so:
  - \( 20 \, \text{menit} = 20 \times 60 = 1200 \, \text{detik} \)
  
Thus, 
\[
72 + 1200 = 1272 \, \text{detik}
\]

### 2. \( \frac{1}{2} \, \text{menit} + 10 \, \text{detik} = \, \, \text{jam} \)

- \( \frac{1}{2} \, \text{menit} = 30 \, \text{detik} \)
- Total seconds = \( 30 + 10 = 40 \, \text{detik} \)
- 1 hour = 3600 seconds, so:
  \[
  40 \, \text{detik} = \frac{40}{3600} \, \text{jam} = \frac{1}{90} \, \text{jam}
  \]
  or approximately \( 0.0111 \, \text{jam} \).

### 3. \( 0.002 \, \text{hm} + 0.01 \, \text{dam} = \, \, \text{km} \)

- 1 hectometer (hm) = 0.1 kilometers (km), so:
  \[
  0.002 \, \text{hm} = 0.002 \times 0.1 = 0.0002 \, \text{km}
  \]
- 1 dekameter (dam) = 0.01 kilometers (km), so:
  \[
  0.01 \, \text{dam} = 0.01 \times 0.01 = 0.0001 \, \text{km}
  \]

Thus, 
\[
0.0002 + 0.0001 = 0.0003 \, \text{km}
\]

### 4. \( 10 \times 10^{-2} \, \text{m} + 4 \times 10^{-4} \, \text{dm} = \, \, \text{cm} \)

- \( 10 \times 10^{-2} \, \text{m} = 0.1 \, \text{m} = 10 \, \text{cm} \) (since 1 m = 100 cm)
- \( 4 \times 10^{-4} \, \text{dm} = 4 \times 10^{-4} \times 10 \, \text{cm} = 0.0004 \times 10 = 0.004 \, \text{cm} \)

Thus, 
\[
10 + 0.004 = 10.004 \, \text{cm}
\]

### 5. \( 0.0004 \, \text{kg} + 10^{-4} \, \text{kg} = \, \, \text{g} \)

- \( 0.0004 \, \text{kg} = 0.0004 \times 1000 = 0.4 \, \text{g} \)
- \( 10^{-4} \, \text{kg} = 10^{-4} \times 1000 = 0.1 \, \text{g} \)

Thus, 
\[
0.4 + 0.1 = 0.5 \, \text{g}
\]

### 6. \( 4.5 \times 10^{-4} \div 2 \times 10^{-6} = \, \, \)

This is a simple division of scientific notation:
\[
\frac{4.5 \times 10^{-4}}{2 \times 10^{-6}} = 2.25 \times 10^{2} = 225
\]

### 7. \( 0.00125 \times 10^{-2} = 0.001 \times 10^{-9} \times 10^{-5} = \, \, \)

- Simplifying both sides:
  \[
  0.00125 \times 10^{-2} = 1.25 \times 10^{-5}
  \]
  and
  \[
  0.001 \times 10^{-9} \times 10^{-5} = 10^{-3} \times 10^{-9} \times 10^{-5} = 10^{-17}
  \]
Thus, 
\[
1.25 \times 10^{-5} = 1.25 \times 10^{-17}
\]

### 8. \( 2 \times 10^{-9} \, \text{jam} - 4 \times 10^{-2} \, \text{menit} = \, \, \)

- \( 4 \times 10^{-2} \, \text{menit} = 4 \times 10^{-2} \times \frac{1}{60} \, \text{jam} = 6.67 \times 10^{-4} \, \text{jam} \)
- Subtracting the two:
  \[
  2 \times 10^{-9} - 6.67 \times 10^{-4} \approx -6.67 \times 10^{-4} \, \text{jam}
  \]

### 9. \( 2 \times 10^{-2} \times 4 \times 10^{-4} \div 2 \times 10^{-5} = \, \, \)

First, multiply the terms in the numerator:
\[
2 \times 4 = 8 \quad \text{and} \quad 10^{-2} \times 10^{-4} = 10^{-6}
\]
Thus, 
\[
\frac{8 \times 10^{-6}}{2 \times 10^{-5}} = 4 \times 10^{-1} = 0.4
\]

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Would you like more details on any of the steps?

Here are five related questions:
1. How do you handle complex unit conversions involving scientific notation?
2. What is the process for converting between different time units, such as minutes to hours?
3. How do you simplify expressions with powers of 10 in scientific notation?
4. What are some common conversions between metric length units (e.g., meters to centimeters)?
5. Can you explain how to manipulate and calculate with small values in scientific notation?

**Tip**: When working with scientific notation, always align powers of 10 and use rules of exponents for easier multiplication or division.

A series of conversion and calculation problems involving time, length, mass, and scientific notation. The user is tasked with solving these unit conversion questions, often using powers of ten.

Learn how to solve unit conversion problems involving time, length, and mass using scientific notation. This step-by-step guide walks through converting hours to seconds, hectometers to kilometers, kilograms to grams, and solving complex expressions with powers of ten.

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