To find the decimal representation of the fraction [tex]\( \frac{2}{10} \)[/tex], let's follow a structured approach:
1. Understanding the Fraction:
- The given fraction is [tex]\( \frac{2}{10} \)[/tex].
- Here, 2 is the numerator (the top part of the fraction).
- 10 is the denominator (the bottom part of the fraction).
2. Performing the Division:
- Division of the numerator by the denominator gives us the decimal form.
- Calculate [tex]\( 2 \div 10 \)[/tex].
3. Simplifying the Calculation:
- To divide 2 by 10, notice that dividing by 10 moves the decimal point one place to the left.
- When you move the decimal point one place left from 2, you get 0.2.
4. Confirming the Value:
- The result of [tex]\( \frac{2}{10} \)[/tex] when computed is 0.2.
5. Selecting the Correct Option:
- We now compare this result with the given options:
- A. 2.10
- B. . 20
- C. . 2
- D. 2.0
- The correct match for our result, 0.2, is option C.
Therefore, the decimal representation of [tex]\( 2 \div 10 \)[/tex] is [tex]\( 0.2 \)[/tex], and the correct answer is:
C. . 2
