Mathematics
Grade 9
15 min
Decimal division patterns over increasing place values
Decimal division patterns over increasing place values
What you'll learn
- Identify corresponding sides in two triangles and determine if the Side-Side-Side (SSS) Congruence Postulate can be applied to prove triangle congruence with 80% accuracy on a formative assessment.
- Apply the Side-Angle-Side (SAS) Congruence Postulate to prove triangle congruence in given geometric diagrams, justifying each step of the proof with appropriate theorems and postulates, and achieving a score of 70% or higher on a problem-solving quiz.
- Explain the difference between SSS and SAS congruence postulates, and provide a counterexample demonstrating why Side-Side-Angle (SSA) is not a valid congruence postulate, in a written explanation graded using a rubric with specific criteria for clarity and accuracy.
- Solve for unknown side lengths or angle measures in a diagram, using SSS or SAS congruence postulates, to justify triangle congruence and correctly determine the missing values in at least 2 out of 3 complex problems involving algebraic expressions.
Tutorial Preview
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Introduction & Learning Objectives
Learning Objectives
Identify the pattern that emerges when a number is divided by increasing powers of 10.
Predict the quotient of a number divided by 10, 100, 1000, etc., without performing long division.
Articulate the relationship between the number of zeros in the divisor and the movement of the decimal point in the dividend.
Represent decimal division problems as rational expressions of the form c / 10^n.
Correctly place leading zeros as placeholders when dividing small numbers by large powers of 10.
Apply these division patterns to evaluate simple rational functions for inputs that are powers of 10.
If a pizza is shared among 10 friends, you get a slice. What happens to your slice if it's shared among 100, or 1,000 friends? 🍕
In this tutorial, we will explore th...
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Key Concepts & Vocabulary
TermDefinitionExample
Place ValueThe value of a digit based on its position in a number. In the decimal system, each place to the left of the decimal is 10 times larger than the one to its right.In 452.3, the '5' is in the tens place, representing 50. The '3' is in the tenths place, representing 3/10.
Power of 10A number that can be written as 10 raised to an integer exponent (n). It's a 1 followed by 'n' zeros.100 is a power of 10 because it can be written as 10^2. 1000 is 10^3.
DividendThe number that is being divided.In the expression 75 ÷ 10, the dividend is 75.
DivisorThe number by which another number is divided.In the expression 75 ÷ 10, the divisor is 10.
QuotientThe result of a division operation.In the expression 75 ÷ 10 = 7.5, the quotient is...
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Core Formulas
Division by Powers of 10
c \div 10^n
To divide a number 'c' by a power of 10 (10^n), move the decimal point in 'c' to the left by 'n' places. The value of 'n' is equal to the number of zeros in the divisor.
Rational Expression Form
c \div x = \frac{c}{x}
Any division problem can be written as a rational expression (a fraction). This is useful for connecting arithmetic patterns to algebraic functions.
Placeholder Zeros
If c < 10^n, then \frac{c}{10^n} < 1
When moving the decimal point to the left, if you run out of digits, add leading zeros between the decimal point and the first non-zero digit as placeholders.
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Challenging
For the function f(x) = 1250/x, what is the smallest integer value of n such that f(10^n) < 0.1?
A.3
B.6
C.4
D.5
Challenging
The number 3456 is divided by 10^n, resulting in the quotient 3.456. This quotient can be interpreted as the sum 3 + 4/10 + 5/100 + 6/1000. What value of n was used in the division?
A.2
B.3
C.4
D.1
Challenging
Consider two functions, f(x) = 8500/x and g(y) = 8.5/y. If f(10^n) = g(10^m), and n = 5, what is the value of m?
A.3
B.2
C.4
D.1
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Decimal division patterns over increasing place values is a Grade 9 Mathematics lesson on ExcelOS.
What will I learn in Decimal division patterns over increasing place values?
You'll be able to: Identify corresponding sides in two triangles and determine if the Side-Side-Side (SSS) Congruence Postulate can be applied to prove triangle congruence with 80% accuracy on a formative assessment; Apply the Side-Angle-Side….
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How many practice questions are included with Decimal division patterns over increasing place values?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.