Question

Question:

Charles, Zayeer, and Kali are trying to simplify
1,000 2/3

​
. Charles says the correct simplification is 10 because 1,000=10⋅10⋅10. Zayeer says the correct simplification is 1,000 because 1,000=10⋅10⋅10→1,000. Kali says the correct simplification is 100 because 1,000=10⋅10→100. Who has the correct value?

Answer Options:

none of them

Charles

Answer 1

To simplify \( 1,000 \frac{2}{3} \), we can start by converting the mixed number into an improper fraction.

1,000 can be written as a fraction:
\[
1,000 = \frac{1,000}{1}
\]

Now, we convert \( 1,000 \frac{2}{3} \) into an improper fraction:
\[
1,000 \frac{2}{3} = 1,000 + \frac{2}{3} = \frac{1,000 \times 3 + 2}{3} = \frac{3,000 + 2}{3} = \frac{3,002}{3}
\]

Now, let's evaluate the simplifications proposed by Charles, Zayeer, and Kali:

- Charles says the correct simplification is **10** because \( 1,000 = 10 \cdot 10 \cdot 10 \). This is incorrect for \( 1,000 \frac{2}{3} \).

- Zayeer says the correct simplification is **1,000**. This is also incorrect for \( 1,000 \frac{2}{3} \).

- Kali says the correct simplification is **100**. This is also incorrect for \( 1,000 \frac{2}{3} \).

Since none of them provided the correct value of \( 1,000 \frac{2}{3} \), which can be expressed as \( \frac{3,002}{3} \) or approximately \( 1,000.67 \), the correct answer is:

**none of them**.