Decimals: Level 1 Challenges


We see that the fractional part of 13\frac{1}{3} is 0.333... It repeats after one digit. Let us say that 13\frac{1}{3} has "period" one. We can also say that 17=0.142857142857142857...\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.





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

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

Note: 0.ab=0.abababab0.\overline{ab}=0.abababab \ldots

(1.2×1.5)0.320.8=? \large (1.2 \times 1.5) - \dfrac{0.32}{0.8} = \, ?

Even though the digits of the decimal 10.5555555555\Large \color{#3D99F6}{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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