Math Problem Statement

Change 4690 mu straight m squared (square mircometres) into straight m squared (square metres).

Question 1Answer

Solution

To convert 4690 square micrometres (µm²) into square metres (m²), follow these steps:

  1. Understand the relationship between units:

    • 1 micrometre (µm) = 10610^{-6} metres (m).
    • Therefore, 1 square micrometre (µm²) = (106)2(10^{-6})^2 m² = 101210^{-12} m².
  2. Convert 4690 µm² to m²:

    = 4.690 \times 10^{-9} \, \text{m}².$$

So, 4690 µm² is equal to 4.690 × 10⁻⁹ m².


Do you need further explanation or clarification? Here are some related questions:

  1. How do you convert other units of area like cm² to m²?
  2. What is the process of converting cubic micrometres (µm³) to cubic metres (m³)?
  3. What are the practical applications of working with square micrometres and square metres?
  4. How does dimensional analysis help in unit conversions?
  5. What is the difference between area and volume conversions?

Tip: Always double-check the powers of 10 when converting between units of area or volume to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Unit Conversion
Area Measurement
Powers of 10

Formulas

1 µm = 10^(-6) m
1 µm² = (10^(-6))^2 m² = 10^(-12) m²
Area in m² = Area in µm² × 10^(-12)

Theorems

Dimensional Analysis

Suitable Grade Level

Grades 8-10