Relating Decimals to Fractions (Grades 4-5)

Many students who come to me for math tutoring are very weak with fraction and decimal concepts. Here are a couple of sample responses from 5th grade students this week.

Q: How can you write 0.15 as a fraction?
A: Is it one-fifth?

Notice that the student tried to write the fraction using the same digits as the decimal.

Q: Write the number two and fifty-four hundredths.
A: 2.54
Follow-up Q: That's right. Can you also write it as a mixed number?
A: No, I don't know how.

Many students have trouble relating decimals to fractions because of inadequate emphasis on decimals as shortcuts for fractions. In Grade 4 of Common Core, there is a high emphasis on fractions in tenths and hundredths, and on meaning of decimals related to fractions. Here are examples of expectations from Common Core 4.NF.5 and 4.NF.6.

• Express fractions in tenths as hundredths.  (i.e. 2/10 is the same as 20/100)
• Add fractions in tenths and hundredths. (i.e. 3/10 + 4/100 = 34/100)
• Convert between decimals and fractions in tenths or hundredths (i.e. 4/10 = 0.4, 0.78 = 78/100)

It is very important that students have a strong understanding of fractions before tackling decimals or students will simply be manipulating digits. They may be getting the correct answers to decimal questions, yet have no idea what the decimals mean. In my tutoring, I emphasize that every number in decimal form is really just a shortcut for a fraction or mixed number.

With students in grades 4-8, I often show them how to change long decimals to fractions. For example, 0.123456789 is the fraction 123,456,789/1,000,000,000. Each digit to the right of the decimal point corresponds to a zero in the denominator of the fraction.