Where the decimal point goes

The idea

In long division, including when the dividend is a decimal, the decimal point is placed in the quotient when Ones are regrouped into Tenths, before the tenths are divided.

Sugar in bags

A shopkeeper has 9.5 kg of sugar and packs it equally into 4 bags. Share the 9 ones: each bag gets 2 and 1 one is left. That 1 one and the 5 tenths make 15 tenths.

In the answer, where does the decimal point go?

• Before the 2, like .2
• After the 2, before we share the tenths
• At the very end, after all the digits

Place the point

Share place by place as before. When you regroup the Ones into Tenths, tap the gold slot to put the decimal point in the quotient. The toy does not let you share tenths without it.

The point goes in with the tenths

The Ones column is on the left of the point and the tenths on the right. The quotient follows the same columns. So the point goes between its Ones and its tenths, before the tenths are shared.

This holds even when the dividend already has a point, as in 9.5 and 0.06. The quotient still needs its own point.

In long division, including when the dividend is a decimal, put the decimal point in the quotient when the Ones are regrouped into Tenths, before the tenths are divided.

• Division | Quotient
• 237 ÷ 8 | 29.625
• 9.5 ÷ 4 | 2.375
• 0.06 ÷ 5 | 0.012

Notes

Put the decimal point in the quotient when the Ones are regrouped into Tenths, before the tenths are divided. This is also so when the dividend has a point.

Check yourself

Find 7.5 ÷ 2 with long division. Type the answer.

Answer: 3.75

3 ones, then the point, then 7 tenths and 5 hundredths: 3.75.

In 8.4 ÷ 3 the quotient digits are 2 and 8: 2 Ones and 8 tenths. Where does the point go?

Find 0.9 ÷ 6. Type the answer.

Answer: 0.15

0 Ones, point, 1 tenth, 5 hundredths: 0.15.

For 0.06 ÷ 5, the dividend already has a decimal point. What about the quotient?

• Between them: 2.8 — correct. The Ones digit is 2, then the point, then the tenths digit 8.
• Before them: 0.28. That makes 2 tenths and 8 hundredths. The 2 is Ones, not tenths.
• After them: 28. That makes 28 Ones. 8.4 ÷ 3 is less than 3.
• It needs no point, because the dividend has one. The quotient has to show where its Ones end too. Otherwise 0012 could mean anything.
• The point goes at the end, after the last digit. The point goes before the tenths are shared, not after all the digits.
• It needs its own point, put in when we move from Ones to Tenths — correct. Yes. After 0 Ones, we put the point in the quotient, then share the tenths.