What does the zero in 0.04 do?

start. A learner writes four hundredths as 0.4. What has changed?

Answer: 0.04 is four hundredths. Writing 0.4 makes the 4 worth four tenths, ten times as much.

Teacher response: Listen for this idea: A zero after the decimal point can always be removed. Follow up: Read the unit named by each column. In 0.04, the zero holds the empty tenths place so the 4 stays in the hundredths column. Removing that zero moves the 4 into another place.

example. A learner writes four hundredths as 0.4. What has changed?

1. Name one whole before comparing any models. A tenth is one of ten equal parts; a hundredth is one of one hundred equal parts of that same whole.
2. Write 0.4 and 0.04 in a chart with the decimal point between ones and tenths. Read them as four tenths and four hundredths.
3. Rename four tenths as forty hundredths. Compare forty hundredths with four hundredths: the first amount is ten times the second.
4. Contrast 0.04 with 0.040. Adding an empty thousandths place at the end does not move the 4; removing the tenths placeholder does.

Worked example: 0.04 is four hundredths. Writing 0.4 makes the 4 worth four tenths, ten times as much.

p1. Write six hundredths as a decimal.

Answer: 0.06

Teacher response: Six hundredths is 6/100; the tenths place is empty.

p2. What is the value of the 7 in 0.07?

Answer: 0.07

Teacher response: The 7 is in the hundredths column.

p3. How many times as large is 0.8 as 0.08?

Answer: 10

Teacher response: Eight tenths is eighty hundredths.

e1. Write five thousandths as a decimal.

Answer: 0.005

Teacher response: Keep empty tenths and hundredths places before the 5.

transfer. Explain why 0.09 and 0.090 are equal but 0.09 and 0.9 are not.

Answer: The final zero adds no thousandths. Removing the zero before the 9 changes nine hundredths to nine tenths.

next. If the learner names a digit without a unit, return to the chart. If the places are secure, compare decimals with different written lengths.