Math Problem Statement

The image contains a series of mathematical problems involving unit conversions, scientific notation, and basic arithmetic operations.

Solution

Let's solve each of the problems shown in the image step-by-step:

1. 0.02 jam+20 menit= detik0.02 \, \text{jam} + 20 \, \text{menit} = \, \text{detik}

  • 1 jam=60 menit=3600 detik1 \, \text{jam} = 60 \, \text{menit} = 3600 \, \text{detik}
  • 0.02 jam=0.02×3600=72 detik0.02 \, \text{jam} = 0.02 \times 3600 = 72 \, \text{detik}
  • 20 menit=20×60=1200 detik20 \, \text{menit} = 20 \times 60 = 1200 \, \text{detik}
  • Total: 72+1200=1272 detik72 + 1200 = 1272 \, \text{detik}

2. 12 menit+10 detik= jam\frac{1}{2} \, \text{menit} + 10 \, \text{detik} = \, \text{jam}

  • 12 menit=0.5×60=30 detik\frac{1}{2} \, \text{menit} = 0.5 \times 60 = 30 \, \text{detik}
  • Total: 30 detik+10 detik=40 detik30 \, \text{detik} + 10 \, \text{detik} = 40 \, \text{detik}
  • Convert to hours: 40 detik=403600=0.0111 jam40 \, \text{detik} = \frac{40}{3600} = 0.0111 \, \text{jam}

3. 0.002 hm+0.01 dam= km0.002 \, \text{hm} + 0.01 \, \text{dam} = \, \text{km}

  • 1 hm=0.1 km1 \, \text{hm} = 0.1 \, \text{km}, so 0.002 hm=0.002×0.1=0.0002 km0.002 \, \text{hm} = 0.002 \times 0.1 = 0.0002 \, \text{km}
  • 1 dam=0.01 km1 \, \text{dam} = 0.01 \, \text{km}, so 0.01 dam=0.01×0.01=0.0001 km0.01 \, \text{dam} = 0.01 \times 0.01 = 0.0001 \, \text{km}
  • Total: 0.0002 km+0.0001 km=0.0003 km0.0002 \, \text{km} + 0.0001 \, \text{km} = 0.0003 \, \text{km}

4. 10×10−2 m+4×10−4 dm= cm10 \times 10^{-2} \, \text{m} + 4 \times 10^{-4} \, \text{dm} = \, \text{cm}

  • 10×10−2 m=10−1 m=0.1 m=10 cm10 \times 10^{-2} \, \text{m} = 10^{-1} \, \text{m} = 0.1 \, \text{m} = 10 \, \text{cm}
  • 4×10−4 dm=4×10−4×10=4×10−3 cm=0.004 cm4 \times 10^{-4} \, \text{dm} = 4 \times 10^{-4} \times 10 = 4 \times 10^{-3} \, \text{cm} = 0.004 \, \text{cm}
  • Total: 10+0.004=10.004 cm10 + 0.004 = 10.004 \, \text{cm}

5. 0.0004 kg+10−4 kg= g0.0004 \, \text{kg} + 10^{-4} \, \text{kg} = \, \text{g}

  • Convert both to grams: 1 kg=1000 g1 \, \text{kg} = 1000 \, \text{g}
  • 0.0004 kg=0.0004×1000=0.4 g0.0004 \, \text{kg} = 0.0004 \times 1000 = 0.4 \, \text{g}
  • 10−4 kg=10−4×1000=0.1 g10^{-4} \, \text{kg} = 10^{-4} \times 1000 = 0.1 \, \text{g}
  • Total: 0.4+0.1=0.5 g0.4 + 0.1 = 0.5 \, \text{g}

6. 4.5×10−4:2×10−6= result4.5 \times 10^{-4} : 2 \times 10^{-6} = \, \text{result}

  • Division: 4.5×10−42×10−6=2.25×102=225\frac{4.5 \times 10^{-4}}{2 \times 10^{-6}} = 2.25 \times 10^2 = 225

7. 0.00125×10−2=0.001×10−9×10−5= result0.00125 \times 10^{-2} = 0.001 \times 10^{-9} \times 10^{-5} = \, \text{result}

  • Simplify the left side: 0.00125×10−2=1.25×10−50.00125 \times 10^{-2} = 1.25 \times 10^{-5}
  • Simplify the right side: 0.001×10−9×10−5=10−3×10−9×10−5=10−170.001 \times 10^{-9} \times 10^{-5} = 10^{-3} \times 10^{-9} \times 10^{-5} = 10^{-17}

8. 2×10−4 jam−4×10−2 menit= result2 \times 10^{-4} \, \text{jam} - 4 \times 10^{-2} \, \text{menit} = \, \text{result}

  • Convert everything to hours:
    • 4×10−2 menit=4×10−2×160=6.67×10−4 jam4 \times 10^{-2} \, \text{menit} = 4 \times 10^{-2} \times \frac{1}{60} = 6.67 \times 10^{-4} \, \text{jam}
  • Subtraction: 2×10−4 jam−6.67×10−4 jam=−4.67×10−4 jam2 \times 10^{-4} \, \text{jam} - 6.67 \times 10^{-4} \, \text{jam} = -4.67 \times 10^{-4} \, \text{jam}

9. 2×10−2×4×10−4:2×10−5= result2 \times 10^{-2} \times 4 \times 10^{-4} : 2 \times 10^{-5} = \, \text{result}

  • Multiplication: 2×10−2×4×10−4=8×10−62 \times 10^{-2} \times 4 \times 10^{-4} = 8 \times 10^{-6}
  • Division: 8×10−62×10−5=0.4\frac{8 \times 10^{-6}}{2 \times 10^{-5}} = 0.4

Would you like further details or clarifications on any of these solutions?

Here are 5 related questions to expand your understanding:

  1. How do you convert time units such as hours, minutes, and seconds?
  2. What is the process of converting between different metric units?
  3. How do you solve problems involving scientific notation and powers of 10?
  4. What are the common mistakes when converting between units?
  5. How can you apply dimensional analysis to check the consistency of units in calculations?

Tip: When working with scientific notation, pay close attention to the exponents, especially when multiplying or dividing values.

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Math Problem Analysis

Mathematical Concepts

Unit conversion (time, distance, mass)
Scientific notation
Basic arithmetic operations (addition, subtraction, multiplication, division)

Formulas

1 hour = 60 minutes = 3600 seconds
1 km = 1000 meters
1 meter = 10 decimeters = 100 centimeters
1 kg = 1000 grams
Scientific notation operations: a x 10^n

Theorems

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Suitable Grade Level

Grades 9-12

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