Dividing by 10, 100, 1000

The idea

To divide a number by 10, 100, 1000, …, move its decimal point (at the end of a counting number) left as many places as the divisor has zeroes, adding zeroes in front if needed.

Jonali’s game

Jonali says a fraction and Pallabi writes the decimal. Jonali says 123/10. That is 123 ÷ 10.

What decimal should Pallabi write?

• 1.23
• 12.3
• 1230

Move the point

A counting number has its decimal point at the end: 123. Press ◀ to move the point one place left. After each move the check line multiplies back. Stop when it matches the number you started with.

One move per zero

One move left makes the number 10 times smaller: that is ÷ 10. So ÷ 100 needs two moves and ÷ 1000 needs three. Count the zeroes in the divisor.

When the point runs past the first digit, zeroes are added in front: 12 ÷ 1000 = 0.012.

To divide a number by 10, 100, 1000, …, write the number with a decimal point at the end. Move the point left as many places as the divisor has zeroes. Add zeroes in front if needed.

• Division | Answer
• 123 ÷ 10 | 12.3
• 24 ÷ 100 | 0.24
• 678 ÷ 1000 | 0.678
• 12 ÷ 1000 | 0.012
• 12345 ÷ 1000 | 12.345

Notes

To divide by 10, 100, 1000, …: move the decimal point left, one place for each zero in the divisor, adding zeroes in front if needed.

Check yourself

What is 345 ÷ 100?

Answer: 3.45

345. → 34.5 → 3.45. Two zeroes, two moves.

What is 7 ÷ 1000?

A rope is 2500 cm long. How many metres is that? (1 m = 100 cm, so divide by 100.)

Answer: 25 m

2500. → 250.0 → 25.00. So 2500 ÷ 100 = 25: a trailing 0 after the point can be dropped.

Meena divides 678 by 1000 and writes 0.0678. What went wrong?

Which is true when we divide 25000 by 10000?

Jonali buys 50 g of cinnamon. Write it in kilograms. 1 kg = 1000 g, so find 50 ÷ 1000.

Answer: 0.05 kg

50. → 5.0 → 0.50 → 0.050. So 50 g = 0.05 kg.

• 0.007 — correct. Yes. Three zeroes, three moves left: 7. → 0.7 → 0.07 → 0.007, with zeroes added in front.
• 0.07. That is only two moves. 1000 has three zeroes.
• 0.7. That is only one move. 1000 has three zeroes.
• She moved the point to the right.. The point did move left. The mistake is how many places it moved.
• She forgot to add a zero in front.. 0.678 needs no extra zero in front: the point passes the first digit exactly.
• She counted the 4 digits of 1000. She should count its 3 zeroes. — correct. Yes. 678 ÷ 1000 = 0.678: three zeroes, three moves.
• The point moves 5 places left, because 10000 has 5 digits.. We count zeroes, not digits: 10000 has 4 zeroes.
• The point moves 4 places right.. Dividing makes a number smaller, so the point moves left.
• The point moves 4 places left, because 10000 has 4 zeroes. — correct. Yes. 25000. → 2.5000 = 2.5.