Egypt Primary 5 Mathematics, Week 11: Dividing by 10, 100 and 1,000

Dividing decimals: powers of ten, models and estimates

Week 11 · Dividing decimals · 3 lessons

Dividing by 10, 100 and 1,000

Discover Mathematics P5: Term 1, Unit 5, Lessons 11–14

GoalDivide a number by 10, 100 or 1,000 by moving its digits to the right, and see how this undoes multiplying.

New words

power of ten · 10, 100, 1,000 … a number made from a 1 followed by zerosinverse operations · two operations that undo each other, such as × 100 and ÷ 100place holder · a zero written so the other digits stay in their places

Explanation

When you divide by 10, every digit moves one place to the right and becomes ten times smaller. Dividing by 100 moves the digits two places and dividing by 1,000 moves them three places. The decimal point does not move; the digits slide past it. Empty places are filled with zeros: 7 ÷ 100 = 0.07. Dividing by a power of ten undoes multiplying by it. Because 0.45 × 100 = 45, we know 45 ÷ 100 = 0.45. Look at the pattern in the table: each time you divide by 10, the number gets one place smaller, so you can keep going down the list without calculating.

Each ÷ 10 moves the digits one place right

Start	÷ 10	÷ 100	÷ 1,000
6,000	600	60	6
80	8	0.8	0.08
3.5	0.35	0.035	—

Worked examples

Number	Hundreds	Tens	Ones	Tenths	Hundredths
3,450 ÷ 10 = 345	3	4	5
3,450 ÷ 100 = 34.5		3	4	5
3,450 ÷ 1,000 = 3.45			3	4	5

A shop has 3,450 g of cheese. 3,450 ÷ 10 = 345, 3,450 ÷ 100 = 34.5 and 3,450 ÷ 1,000 = 3.45. The digits 3, 4, 5 and 0 keep their order and only the point seems to move.

8 ÷ 100 = 0.08

Ones	Tenths	Hundredths
0	0	8

A rope 8 m long is cut into 100 equal pieces. 8 ÷ 100 = 0.08, so each piece is 0.08 m, which is 8 cm. There are no tenths, so a 0 holds the tenths place.

★Remember

× 100 and ÷ 100 undo each other. So if you know one, you know the other.

Find the number: □ × 100 = 73. Division undoes multiplication, so □ = 73 ÷ 100 = 0.73. Check: 0.73 × 100 = 73.

Class activity

Digit-shift race. Start with 4,800 on a piece of paper. Take turns rolling a die: 1 or 2 means ÷ 10, 3 or 4 means ÷ 100, 5 or 6 means ÷ 1,000. Divide the current number and write the result below. Stop when someone reaches a number smaller than 1 and read it aloud with its place names.

Practice

Work out 520 ÷ 10, 520 ÷ 100 and 520 ÷ 1,000.

Work out 7.8 ÷ 10, 91 ÷ 100 and 6 ÷ 1,000.

A bag of 12 kg of flour is shared equally into 1,000 tiny packs. How many kg is one pack? How many grams?

Find the missing number: □ ÷ 100 = 0.39.

Hana says 25 ÷ 10 = 0.25. What did she do wrong? Give the right answer.