To determine which sign makes the statement true between \(9 \frac{3}{10}\) and \(9 \frac{2}{5}\), we first need to convert both mixed numbers into improper fractions or decimal form for easier comparison.
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Convert \(9 \frac{3}{10}\) to decimal: \[ 9 \frac{3}{10} = 9 + 0.3 = 9.3 \]
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Convert \(9 \frac{2}{5}\) to decimal: \[ 9 \frac{2}{5} = 9 + 0.4 = 9.4 \]
Now we can compare the two decimal values:
- \(9.3\) (for \(9 \frac{3}{10}\))
- \(9.4\) (for \(9 \frac{2}{5}\))
This means:
\[ 9 \frac{3}{10} < 9 \frac{2}{5} \]
So the correct sign is: \[ 9 \frac{3}{10} < 9 \frac{2}{5} \]
Thus, the statement is true with the less-than sign (\(<\)).