Why are 0.6 and 0.60 equal?

start. Does writing 0.60 instead of 0.6 make the amount larger?

Answer: No. Six tenths and sixty hundredths describe the same share of the same whole.

Teacher response: Listen for this idea: The number with more digits must be larger. Follow up: Count the unit as well as the digits. Sixty hundredths uses ten times as many pieces, but each piece is one tenth as large as a tenth.

example. Does writing 0.60 instead of 0.6 make the amount larger?

1. Shade six parts of a whole divided into ten equal parts. Leave the four unshaded tenths visible.
2. Split every tenth into ten equal pieces, including the unshaded parts. The whole now contains one hundred equal pieces.
3. The six shaded tenths contain sixty hundredths. The shaded endpoint and the reference whole have not moved.
4. Write 6/10 = 60/100, then 0.6 = 0.60. A final zero can extend the notation without changing value; a zero inserted before the 6 would move it to another place.

Worked example: No. Six tenths and sixty hundredths describe the same share of the same whole.

p1. How many hundredths are in 0.7?

Answer: 70

Teacher response: Seven tenths contains seventy hundredths.

p2. Compare 0.30 and 0.3. Enter <, = or >.

Answer: =

Teacher response: Both represent three tenths.

p3. Write 40/100 as a decimal.

Answer: 0.40

Teacher response: Forty hundredths can be written 0.40 or 0.4.

e1. Compare 0.05 and 0.5. Enter <, = or >.

Answer: <

Teacher response: Five hundredths is less than fifty hundredths. This zero is a placeholder, not a final zero.

transfer. Explain how ten tenths can also be called one hundred hundredths.

Answer: Each of the ten tenths contains ten hundredths, so the same whole contains 10 × 10 = 100 hundredths.

next. If the learner counts pieces without naming their size, align the two wholes and compare endpoints. Then move to decimal comparisons.