Dividing a decimal by tens

Anuja has a ribbon 3.9 m long and wants to cut it into 10 equal pieces. How long is each piece?

Since there are 10 pieces, divide 3.9 by 10. Convert the decimal to a fraction: 3.9 = 39/10. So we need 39/10 ÷ 10.

Recall that dividing a fraction by a divisor is the same as multiplying by the RECIPROCAL of that divisor. The reciprocal of 10 is 1/10.

So 39/10 ÷ 10 = 39/10 × 1/10 = 39/100 = 0.39. Each piece of ribbon is 0.39 m long.

Now cut the same ribbon into 100 equal pieces instead: 3.9 ÷ 100 = 39/10 × 1/100 = 39/1000 = 0.039. Each piece is 0.039 m — which, if you prefer, is 3.9 cm or 39 mm.

Look at the two answers beside the original number: 3.9, then 0.39, then 0.039. The digits have not changed at all; only the position of the point has. An easy way to remember: dividing by 10s slides the point left (the number gets smaller); multiplying by 10s slides it right (the number gets bigger).

So the rule for dividing a decimal by 1, 10, 100, 1000 and so on is exactly the rule you had for whole numbers: Move the decimal point to the left by as many places as there are zeroes in the divisor. For 18.7: divide by 10 for 1.87, by 100 for 0.187, by 1000 for 0.0187, by 10000 for 0.00187.