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Division by Powers of Ten
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Division by Powers of Ten
Divide by 10, 100 or 1,000. Show your working where space is provided. Remember: dividing by a power of ten makes a number smaller by shifting its digits to lower place-value positions.
Place value patterns
1.Calculate each quotient: 6,300 ÷ 10; 6,300 ÷ 100; 6,300 ÷ 1,000.
2.When a number is divided by 10, which way do its digits shift in a place-value chart?
- One place to the left
- One place to the right
- Two places to the left
- They do not shift
3.Dividing by 1,000 shifts each digit how many places, and in which direction?
Money and everyday sharing
4.A city bus route fundraiser raises $3,600. The money is shared equally among 100 contributors. How much does each contributor receive?
5.A transport company divides $7,200 of its budget equally between 10 service areas. What amount goes to each area?
6.Choose the correct result for $9,400 ÷ 1,000.
- $94
- $9.40
- $0.94
- $940
Measurement conversions
7.A bus route is 5,000 metres long. Convert this distance to kilometres by dividing by 1,000.
8.A delivery contains 4,800 grams of rice. How many kilograms of rice is that?
9.Match each division calculation with its answer: 8,000 m ÷ 1,000; 650 cm ÷ 100; 5,400 g ÷ 1,000. Answers: 5.4 kg, 8 km, 6.5 m.
- 8,000 m ÷ 1,000
- 650 cm ÷ 100
- 5,400 g ÷ 1,000
- 6.5 m
- 5.4 kg
- 8 km
Estimate, calculate and explain
10.For each calculation, give an estimate to the nearest whole number and then find the exact answer: a) 846 ÷ 100; b) 7,350 ÷ 10; c) 6,800 ÷ 1,000.
11.Select every useful strategy for dividing by powers of ten.
- Track digit values in a place-value chart
- Use the decimal-point shift as a shortcut
- Estimate to check whether the result is sensible
- Multiply by 10 instead
- Recognise that dividing by 100 is the same as multiplying by 0.01
Problem solving and quick check
12.Nathan counts 9,600 tickets for a city bus route event. He packs 10 tickets in each bundle, then puts 100 bundles in each carton. How many bundles are there, and how many full cartons can be packed?
13.Explain why dividing 4.8 by 100 gives 0.048. Refer to the place value of the digits.
14.Fill each blank: ___ ÷ 10 = 63.4; 4,500 ÷ ___ = 45; ___ ÷ 1,000 = 0.82.
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