Multiplying and Dividing Decimals by 10, 100 and 1000

The Story

Anaya's cousin Priya worked at a hospital lab and had been invited to show the class how real measurements worked. She held up a tiny vial. "This holds 0.045 litres. I need to write that on the label in millilitres. Watch."

She wrote 0.045, then simply slid the decimal point three places to the right, adding zeros where she ran out of digits: 45.

"That's it?" said Kabir. "No working?"

"There's a rule underneath it. A litre is 1000 millilitres, so converting is multiplying by 1000. Watch what actually happens when you multiply by 1000 the long way."

She wrote 0.045 × 10 = 0.45 on the board, then 0.45 × 10 = 4.5, then 4.5 × 10 = 45. Three separate multiplications by 10, one after another.

"Every time you multiply by 10, every digit shifts one place to the left — which looks exactly like the decimal point sliding one place to the right. Do it three times because 1000 is 10 three times over, and the point moves three places."

Anaya tried it the other way: 250 millilitres, converted back to litres — dividing by 1000. "So the point goes left three places instead. 250 becomes 0.25."

"Exactly. Multiplying makes a number bigger, so the point moves right, away from a smaller value. Dividing makes it smaller, so the point moves left."

Kabir tried a trickier one: 7 divided by 1000. "There's nowhere for the point to slide from — 7 doesn't have decimal places yet."

"Give it some," said Priya. "7 is 7.000. Now slide the point three places left: 0.007. You padded with zeros exactly like you would for addition."

Priya packed the vial away. "In the lab this isn't a trick — it's the only way to convert fast enough to matter. A doctor waiting for a dosage doesn't have time for long multiplication."