Mathematics
Grade 9
15 min
Divide numbers ending in zeroes: word problems
Divide numbers ending in zeroes: word problems
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1
Introduction & Learning Objectives
Learning Objectives
Translate real-world scenarios into division problems involving numbers with trailing zeroes.
Apply the 'zero cancellation' shortcut to efficiently divide large numbers ending in zeroes.
Utilize powers of 10 and scientific notation to simplify and solve complex division word problems.
By the end of of this lesson, students will be able to interpret the quotient and any remainder in the context of the original word problem.
Verify the reasonableness of their answers through estimation and inverse operations.
Solve multi-step problems that require dividing numbers ending in zeroes as an intermediate step.
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Key Concepts & Vocabulary
TermDefinitionExample
DividendThe number that is being divided. In a word problem, this is the total amount you are starting with.In 'A company's $5,000,000 profit is shared among 50 employees', the dividend is 5,000,000.
DivisorThe number by which the dividend is being divided. In a word problem, this is the number of groups or the size of each group you are splitting the total into.In 'A company's $5,000,000 profit is shared among 50 employees', the divisor is 50.
QuotientThe result of a division problem.The quotient of 800 ÷ 40 is 20.
Trailing ZeroesA sequence of zeroes at the end of an integer. These zeroes are significant because they represent multiples of powers of 10.The number 72,000 has three trailing zeroes.
Powers of 10Numbers that can be expresse...
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Core Formulas
Zero Cancellation Rule
For a dividend ending in 'm' zeroes and a divisor ending in 'n' zeroes, you can cancel out min(m, n) zeroes from both numbers before dividing.
This is a shortcut for dividing both the dividend and divisor by the same power of 10. Use it to simplify the problem before performing the core division. For example, 64,000 ÷ 800 becomes 640 ÷ 8.
Division using Powers of 10
\frac{a \times 10^m}{b \times 10^n} = \frac{a}{b} \times 10^{m-n}
This is the formal algebraic rule behind zero cancellation. Express the numbers in a form similar to scientific notation, divide the base numbers (a/b), and subtract the exponents of 10. This is especially useful when the numbers are very large and already in scientific notation.
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Challenging
A corporation's total revenue is R = 5.4 x 10⁹ dollars, generated by N = 9 x 10⁴ employees. Which expression correctly represents the calculation for the average revenue per employee, applying the division rule for powers of 10?
A.(5.4 / 9) x 10⁹⁺⁴
B.(5.4 x 9) x 10⁹⁻⁴
C.(5.4 / 9) x 10⁹⁻⁴
D.(9 / 5.4) x 10⁴⁻⁹
Challenging
The mass of the Earth is approximately 6.0 x 10²⁴ kg. A large asteroid has a mass of 3.0 x 10¹⁹ kg. If the Earth's mass were divided into chunks the size of this asteroid, and these chunks were then distributed equally among 200,000 research teams, approximately how many chunks would each team receive?
A.1,000,000
B.10,000
C.1,000
D.100
Challenging
A student is asked to solve: 'A national lottery prize of $140,000,000 is to be split among 700 winners.' The student's work is: Step 1: 140,000,000 / 700. Step 2: 14,000,000 / 7. Step 3: Result is 2,000,000. Which common pitfall did the student fall into?
A.Incorrect Zero Cancellation
B.Misidentifying Dividend and Divisor
C.Ignoring Non-Zero Digits in the Divisor
D.Losing Track of Place Value
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