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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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