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In this problem you're being asked to take a decimal and turn it into a fraction. We need only picture this as money to convert.
If this were money we would have $23.80. We know the whole number of dollars is 23, so this would be the whole number in our fraction. We still have 80 cents, which we know to be 80/100 (100 pennies makes a whole dollar). We can simplify the 80/100 by removing common zeros, which makes 80 become 8 and 100 become 10. So our last part becomes 8/10. Thus our current mixed number is 23 and 8/10.
Hold on though, 8/10 can be simplified further, otherwise this mixed number is an unsimplified fraction, which in many ways makes it still improper. 8/10 is the same as 4/5 (8/10)/(2/2) = (8/2)/(10/2) = 4/5. Therefore the proper simplified mixed number for 23.8 is 23 and 4/5
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