Decimal Darts

And so it came to pass. As soon as the decimal numbers in the 'burg learned they have family in Number Town, they packed their gear and headed for the mountains and beyond to Number Town where they learned that Decimal Darts just opened in Fraction Arcade. When they arrived, Mayor 1 was there to greet them. After they settled in, the Mayor told them that the decimal darts extravaganza was ready to go. Now everyone was new to the game so a bit of an overview was appropriate. The game is similar to Fraction Darts except this time you enter decimal numbers to try to hit the balloons. On the left is an example of what could occur: 0.6 is too small and 0.7 is too big. Keep in mind what you learned from .4 (which could also be written as 0.4 but citizens of Decimalburg left off the zero when it's clear where the decimal point goes.) .6 is the same as 6/10 and .7 is the same as 7/10. So the question is what's a decimal between 6/10 and 7/10? You could say that since 6 1/2 is between 6 and 7 you could use a complex fraction like this: That's pretty ugly. There's got to be a better way! Indeed. What if we use a fraction with a 100 in the bottom? If we clone the ugly one up above by 10 we get: What? asks .4 Complex fractions? What are you talking about? 7/10ths who was in the crowd had an aha moment and said "Look at result. How do you read that? Why, 65 hundredths said the Mayor. But that's what I would say in the 'burg interrupts .4 and I would write it as .65 So point 65 is the same as 65/100 said the Mayor. That's between .6 and .7