Question
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\( \frac{1}{10} \) cubed

Ask by Schwartz Wilson. in the United States
Jan 23,2025

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Tutor-Verified Answer

Answer

\[ \left( \frac{1}{10} \right)^3 = \frac{1}{1000} = 0.001 \]

Solution

To calculate \( \left( \frac{1}{10} \right)^3 \), follow these steps: 1. **Understand the Expression:** The expression \( \left( \frac{1}{10} \right)^3 \) means you are multiplying \( \frac{1}{10} \) by itself three times: \[ \left( \frac{1}{10} \right) \times \left( \frac{1}{10} \right) \times \left( \frac{1}{10} \right) \] 2. **Multiply the Numerators and Denominators:** - **Numerators:** \( 1 \times 1 \times 1 = 1 \) - **Denominators:** \( 10 \times 10 \times 10 = 1000 \) 3. **Combine the Results:** \[ \frac{1}{1000} \] 4. **Convert to Decimal (Optional):** \[ \frac{1}{1000} = 0.001 \] **Final Answer:** \[ \left( \frac{1}{10} \right)^3 = \frac{1}{1000} = 0.001 \]

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The Deep Dive

Cubing \( \frac{1}{10} \) means multiplying \( \frac{1}{10} \) by itself three times: \[ \left( \frac{1}{10} \right)^3 = \frac{1}{10} \times \frac{1}{10} \times \frac{1}{10} = \frac{1}{1000}. \] So, \( \frac{1}{10} \) cubed equals \( \frac{1}{1000} \)! Fun fact: \( \frac{1}{1000} \) is also equivalent to 0.001. This tiny decimal is often used in various fields, like science and engineering, to represent very small quantities. You might think of it as a "kilo" in reverse—just a little fraction that fits snugly in a bigger picture! Another interesting tidbit: Cubing fractions is common in geometry, especially when calculating the volume of cubes! For instance, if you have a cube with a side length of \( \frac{1}{10} \) meters, the volume will be \( \frac{1}{1000} \) cubic meters—perfect for tiny spaces in model buildings or miniature designs!

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