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## Decimals

Coins are often used to express a fraction of a currency. In the US, a quarter is $0.25 and a dime is$0.10. Counting change is just one of many ways you can put decimals to use in everyday life.

# Level 1

We see that the fractional part of $$\frac{1}{3}$$ is 0.333... It repeats after one digit. Let us say that $$\frac{1}{3}$$ has "period" one. We can also say that $$\frac{1}{7} = 0.142857142857142857...$$ has "period' six. Which of the following has the longest "period'?

Order these decimals and fractions. Your answer should be the largest one followed by the smallest one.

$\dfrac{3}{4}$

$.83$

$\dfrac{86}{100}$

$.79$

PS. The numbers aren't in order for biggest and smallest

$\large \displaystyle {0. \overline{42}-0.\overline{35}= \ ?}$

Note: $$0.\overline{ab}=0.abababab \ldots$$

$\large (1.2 \times 1.5) - \dfrac{0.32}{0.8} = \, ?$

Even though the digits of the decimal $\Large \color{blue}{10.5555555555}\ldots$ repeat forever, it can be written a simple fraction! Which of these fractions is equivalent to this decimal number?

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