From what I've seen, recurring decimal questions seem to focus on two skills:
- convert between decimal and fractional form
- compare their size with other numbers
But why do we not explore them in greater detail? Recurring decimals are numbers - they can be used anywhere that numbers appear!
This worksheet has 10 questions which include recurring decimals in other topics. I've found that the additional time working with recurring decimals helps students to appreciate that they are just numbers and gain more confidence with the topic. By working on harder questions, students begin to see the "standard exam questions" as being relatively simple in comparison to these cross-topic questions.
Multiply the lengths to find the volume\[3.\dot{5}\times2.25\times1.2=3\frac{5}{9}\times\frac{9}{4}\times\frac{6}{5}=\frac{32}{9}\times\frac{9}{4}\times\frac{6}{5}=\frac{48}{5}\]Convert the density to an improper fraction\[8.7=8\frac{7}{9}=\frac{79}{9}\]Multiply the volume and density to find the mass\[\frac{48}{5}\times\frac{79}{9}=\frac{3792}{45}\]We can convert that the a recurring decimal to give us a mass in grams.\[3792\div45=82.4\dot{6}\]
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