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Fraction Classroom · 2.2.0 · Teacher answers & responses

Choose the denominator when turning a decimal into a fraction

Use the last named place to choose tenths or hundredths, and check that the fraction keeps the same value.

One whole has one hundred equal parts. Thirty-five parts are selected.0.35 = 35/100
One whole has one hundred equal parts. Thirty-five parts are selected.

Discuss the opening question

start. Why is 0.35 equal to 35/100 rather than 35/10?

Answer: 0.35 means thirty-five hundredths. The final digit is in the hundredths place, so the written decimal fraction is 35/100.

Teacher response: Listen for this idea: Every number after a decimal point can be put over ten. Follow up: Read the place-value unit. A single decimal place names tenths; two decimal places can be read together as hundredths. The number of written digits is useful only because it identifies that place.

Work through the explanation

example. Why is 0.35 equal to 35/100 rather than 35/10?

  1. Read 0.35 as three tenths and five hundredths. Rename the three tenths as thirty hundredths.
  2. Combine the parts: thirty hundredths plus five hundredths makes thirty-five hundredths. Write 35/100.
  3. Read the denominator as the unit: one hundred equal parts make the whole, and thirty-five are selected. Keep 35/100 as the decimal fraction; simplifying is not needed for this task.
  4. Check the magnitude. 0.35 is below one, but 35/10 is 3.5, above three. A denominator choice that changes the size cannot be right.

Worked example: 0.35 means thirty-five hundredths. The final digit is in the hundredths place, so the written decimal fraction is 35/100.

Practise, then check independently

Use p1–p3 for practice. Try e1 without help. Show how your place-value units or model support the result.

p1. Write 0.45 as a fraction. Any equivalent fraction is accepted.

Answer: 45/100

Teacher response: Forty-five hundredths is 45/100.

p2. Write 0.08 as a fraction. Any equivalent fraction is accepted.

Answer: 8/100

Teacher response: Eight hundredths is 8/100.

p3. Write 3/10 as a decimal.

Answer: 0.3

Teacher response: Three tenths uses one decimal place.

e1. Write 0.6 as a fraction. Any equivalent fraction is accepted.

Answer: 6/10

Teacher response: Six tenths is 6/10, also 60/100 or 3/5.

Explain a new situation

transfer. A learner writes 0.50 as 50/100 and another writes 5/10. Can both be correct?

Answer: Yes. Fifty hundredths and five tenths are both one half of the same whole. The fraction forms are different but equivalent.

Choose the next teaching move

next. If the denominator is chosen mechanically, read the decimal aloud using its unit and draw it on a hundredths model. Simplification is optional here.

Teaching notes