Math Problem Statement

7.) (5 pts. each) Show your work for each problem. a.) Convert: 7 m^2 = _______ mm^2 b.) Convert: 228 mL = _______ L

Solution

Let's solve each part.

Part (a)

Convert 7m27 \, \text{m}^2 to mm2\text{mm}^2.

To go from meters to millimeters in area, each meter needs to be converted twice due to the squared units:

  1. 1 meter = 1000 millimeters (1 m = 10310^3 mm).
  2. Therefore, 1m2=(103)2mm2=106mm21 \, \text{m}^2 = (10^3)^2 \, \text{mm}^2 = 10^6 \, \text{mm}^2.

Now, multiply 7m27 \, \text{m}^2 by 10610^6: 7m2=7×106mm2=7,000,000mm27 \, \text{m}^2 = 7 \times 10^6 \, \text{mm}^2 = 7,000,000 \, \text{mm}^2

Answer for (a):

7m2=7,000,000mm27 \, \text{m}^2 = 7,000,000 \, \text{mm}^2


Part (b)

Convert 228mL228 \, \text{mL} to liters (L).

Using the metric conversion, 1L=1000mL1 \, \text{L} = 1000 \, \text{mL}, so: 228mL=2281000L=0.228L228 \, \text{mL} = \frac{228}{1000} \, \text{L} = 0.228 \, \text{L}

Answer for (b):

228mL=0.228L228 \, \text{mL} = 0.228 \, \text{L}

Would you like further details on these conversions or have any questions?


Related Questions:

  1. How would you convert square centimeters to square meters?
  2. How many cubic centimeters are in a cubic meter?
  3. What is the volume in liters of 1000 milliliters?
  4. How does converting cubic units differ from converting square units?
  5. If 1 liter = 1000 milliliters, how would you express 500 milliliters in liters?

Tip: When converting squared or cubic units, remember to apply the conversion factor for each dimension separately. For example, converting m² to cm² requires squaring the factor for m to cm.

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Math Problem Analysis

Mathematical Concepts

Metric Unit Conversion
Area Conversion
Volume Conversion

Formulas

1 m = 1000 mm, therefore 1 m^2 = (1000 mm)^2 = 10^6 mm^2
1 L = 1000 mL, therefore 228 mL = 228 / 1000 L

Theorems

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Suitable Grade Level

Grades 6-8