Divide by ten without losing a placeholder

start. What happens when 3.6 is divided into ten equal shares?

Answer: Each share is 0.36. Three ones become three tenths per share, and six tenths become six hundredths per share.

Teacher response: Listen for this idea: Remove a zero or erase a digit when dividing by ten. Follow up: Division changes the size of the quantity; it does not delete information. Track each digit as its unit becomes one tenth as large.

example. What happens when 3.6 is divided into ten equal shares?

1. Read 3.6 as three ones and six tenths. Keep both contributions visible.
2. Divide each contribution by ten: three ones become three tenths, and six tenths become six hundredths.
3. Write 0.36 and multiply it by ten to recover 3.6. The zero before the point names zero whole units.
4. When the result has an empty tenths place, record a zero there too. For example, 0.4 ÷ 10 = 0.04.

Worked example: Each share is 0.36. Three ones become three tenths per share, and six tenths become six hundredths per share.

p1. Calculate 4.8 ÷ 10.

Answer: 0.48

Teacher response: Four ones become four tenths; eight tenths become eight hundredths.

p2. Calculate 0.7 ÷ 10.

Answer: 0.07

Teacher response: Seven tenths become seven hundredths.

p3. Calculate 6 ÷ 100.

Answer: 0.06

Teacher response: Six hundredths is 6/100.

e1. Calculate 0.08 ÷ 10.

Answer: 0.008

Teacher response: Eight hundredths become eight thousandths.

transfer. How can multiplication check the result of 2.5 ÷ 100?

Answer: The result is 0.025. Multiplying 0.025 by 100 gives 2.5, recovering the starting amount.

next. If a nonzero digit disappears, reconstruct the starting quantity with multiplication. If secure, alternate multiplication and division by powers of ten.