Math Problem Statement

Convert the following, show steps including the ratios or factors used: 38 km = ______ meters 384 dm = ______ millimeters 5 meters = ______ hectometers 7 dam = ______ centimeters 4 km = ______ centimeters 12 meters = ______ millimeters

Solution

Let’s go through each conversion step-by-step:

1. 38 \, \text{km} = \, \text{______ meters}

1 kilometer (km) = 1000 meters (m).

38km=38×1000=38000meters38 \, \text{km} = 38 \times 1000 = 38000 \, \text{meters}

Answer: 38km=38000meters38 \, \text{km} = 38000 \, \text{meters}


2. 384 \, \text{dm} = \, \text{______ millimeters}

1 decimeter (dm) = 100 millimeters (mm).

384dm=384×100=38400millimeters384 \, \text{dm} = 384 \times 100 = 38400 \, \text{millimeters}

Answer: 384dm=38400millimeters384 \, \text{dm} = 38400 \, \text{millimeters}


3. 5 \, \text{meters} = \, \text{______ hectometers}

1 meter (m) = 0.01 hectometers (hm).

5meters=5×0.01=0.05hectometers5 \, \text{meters} = 5 \times 0.01 = 0.05 \, \text{hectometers}

Answer: 5meters=0.05hectometers5 \, \text{meters} = 0.05 \, \text{hectometers}


4. 7 \, \text{dam} = \, \text{______ centimeters}

1 dekameter (dam) = 1000 centimeters (cm).

7dam=7×1000=7000centimeters7 \, \text{dam} = 7 \times 1000 = 7000 \, \text{centimeters}

Answer: 7dam=7000centimeters7 \, \text{dam} = 7000 \, \text{centimeters}


5. 4 \, \text{km} = \, \text{______ centimeters}

1 kilometer (km) = 100,000 centimeters (cm).

4km=4×100000=400000centimeters4 \, \text{km} = 4 \times 100000 = 400000 \, \text{centimeters}

Answer: 4km=400000centimeters4 \, \text{km} = 400000 \, \text{centimeters}


6. 12 \, \text{meters} = \, \text{______ millimeters}

1 meter (m) = 1000 millimeters (mm).

12meters=12×1000=12000millimeters12 \, \text{meters} = 12 \times 1000 = 12000 \, \text{millimeters}

Answer: 12meters=12000millimeters12 \, \text{meters} = 12000 \, \text{millimeters}


Would you like more details on any of these conversions, or do you have any questions?

Here are some related questions that might expand on this topic:

  1. How do you convert meters to kilometers, and vice versa?
  2. What is the relationship between decimeters and centimeters?
  3. How would you convert kilometers to millimeters directly?
  4. What is the factor for converting hectometers to kilometers?
  5. How do you verify the accuracy of your conversions in different units?

Tip: Remember, to convert up or down in the metric system, you can use powers of ten based on the metric prefixes.

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Math Problem Analysis

Mathematical Concepts

Unit Conversion
Metric System

Formulas

1 km = 1000 meters
1 dm = 100 millimeters
1 meter = 0.01 hectometers
1 dam = 1000 centimeters
1 km = 100,000 centimeters
1 meter = 1000 millimeters

Theorems

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Suitable Grade Level

Grade 5-7