Common misconceptions with decimals and fractions

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Concepts such as the mole are hard enough to understand on their own before adding in the further complication of manipulating the actual numbers.

Want to know more about the mole? To explore this topic in more detail subscribe to the Quantitative chemistry course (Understanding the mole).

Decimals and fractions can cause some students real problems, which can in turn become barriers to learning in chemistry. As chemistry teachers it is helpful to be aware of some of the common misconceptions and misunderstanding in maths, so we can help students to make progress. Here are a few of the common ones to look out for.

Misconception 1: Multiplying decimals

Student answer: since 1 x 1 = 1 then by comparison 0.1 x 0.1 = 0.1

The correct answer is 0.01 as you are actually multiplying

\inline \dpi{100} \frac{1}{10}\: \: by\: \: \frac{1}{10}

which means   \inline \dpi{100} \frac{1}{10}\times \frac{1}{10}

So this has a value of \inline \dpi{100} \frac{1}{100}  or 0.01 as a decimal.

Misconception 2: Decimals and their equivalent fractions

Decimals and fractions are different types of numbers. Therefore there is no equivalent fraction for any decimal number.

For an explanation revisit the significant figures page.

Misconception 3: Dividing whole numbers by fractions

Student answer: the value of \inline \dpi{100} 6\div \frac{1}{3} is equivalent to 6 ÷ 3 and therefore has a value of 2.

The division of \inline \dpi{100} 6\div \frac{1}{3} means how many \inline \dpi{100} \frac{1}{3} are there in the number 6. Clearly there are 3 thirds in 1 and hence 3 x 6 (=18) in 6.

 

 

So \inline \dpi{100} 6\div \frac{1}{3}= 18

Students find it difficult to divide by a fraction. Putting the problem into a familiar context such as dividing a cake between a certain number of people can help. You can also remind them of the rules learnt in maths for dividing by a fraction, ie turn the fraction 'upside down' and then multiply.

In the article,  ‘Fractions: fear and loathing in mathematics’ , Paul Yates discusses further some of the common misconceptions and misunderstandings encountered when dealing with fractions. He then goes on to provide some examples in chemistry including:

  • mole fractions
  • spectroscopy of hydrogen-like atoms
  • Arrhenius equations.

Read through the Paul Yates article and consider how an appreciation of these common misconceptions and misunderstandings will affect your future teaching of these topics. 

 
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