Mathematics
Grade 9
15 min
Division with decimal quotients and rounding (Practice on workbooks)
Division with decimal quotients and rounding (Practice on workbooks)
What you'll learn
- Identify corresponding sides and angles in two congruent triangles given a diagram or a congruence statement, and justify their congruence using the definition of CPCTC (Corresponding Parts of Congruent Triangles are Congruent).
- Apply the CPCTC theorem to prove that specific sides or angles in two triangles are congruent after establishing triangle congruence using postulates such as SSS, SAS, ASA, and AAS.
- Construct logical and coherent two-column proofs to demonstrate the congruence of specific line segments or angles within geometric figures, justifying each step using postulates, theorems, and the CPCTC theorem.
- Solve geometric problems, including those involving overlapping triangles or auxiliary lines, by strategically applying CPCTC in conjunction with other geometric theorems and postulates to deduce unknown angle measures or side lengths.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Perform long division with whole numbers or decimals that results in a decimal quotient.
Identify when a division problem will result in a terminating or repeating decimal.
Apply standard rounding rules to a specified place value (e.g., tenths, hundredths).
Calculate the value of a simple rational expression for a given input, resulting in a decimal that requires rounding.
Solve word problems that require division and rounding of the final answer to a practical number of decimal places.
Accurately interpret the remainder in a division problem and express it as a decimal by adding zeros to the dividend.
Use a calculator to verify division results and practice rounding skills.
Ever tried to split a pizza bill of $47.50 among 3 friends and got a never-endi...
2
Key Concepts & Vocabulary
TermDefinitionExample
QuotientThe result obtained by dividing one quantity by another.In the problem 15 ÷ 3 = 5, the number 5 is the quotient.
DividendThe number that is being divided.In the problem 15 ÷ 3 = 5, the number 15 is the dividend.
DivisorThe number by which another number is to be divided.In the problem 15 ÷ 3 = 5, the number 3 is the divisor.
Decimal QuotientA quotient that includes a decimal point because the division does not result in a whole number.The result of 9 ÷ 4 is the decimal quotient 2.25.
Terminating DecimalA decimal number that has a finite number of digits after the decimal point.5 ÷ 8 = 0.625. The decimal ends at the thousandths place.
Repeating DecimalA decimal number that has a digit or a block of digits that repeats infinitely.2 ÷ 3 = 0.666... which can be w...
3
Core Formulas
The Division Algorithm
For any dividend `a` and non-zero divisor `b`, `a / b = q`, where `q` is the quotient.
This is the fundamental principle of division. When a decimal quotient is needed, we add a decimal point and trailing zeros to the dividend and continue the division process until the remainder is zero or we have enough decimal places to round accurately.
The Rounding Rule
1. Identify the rounding digit. 2. Look at the digit to its right. 3. If the digit to the right is 5 or greater, add 1 to the rounding digit. 4. If it's 4 or less, leave the rounding digit. 5. Drop all digits to the right.
Use this rule to approximate a decimal quotient to a required level of precision, such as the nearest tenth or hundredth.
Evaluating a Rational Expression
For a ration...
4 more steps in this tutorial
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Sign Up Free to ContinueSample Practice Questions
Challenging
The cost to produce `x` items in a factory is given by the function C(x) = 10x + 75. The average cost per item is given by the rational function A(x) = C(x) / x. What is the average cost per item if 20 items are produced, rounded to the nearest cent?
A.$13.70
B.$13.80
C.$13.75
D.$14.00
Challenging
A number `n` is divided by 8. The result is then rounded to the nearest hundredth, giving an answer of 2.13. Which of the following could be the original number `n`?
A.16.9
B.17.04
C.17.08
D.17.1
Challenging
To evaluate f(x) = 1 / (x - 2) for x = 5, a student calculates 1 ÷ 3 and gets 0.333... They write down 0.33 and state this is the answer rounded to the nearest hundredth. What is the correct value rounded to the nearest hundredth, and what pitfall did the student make?
A.0.33; The student made no error.
B.0.34; The student rounded too early.
C.0.30; The student misplaced the decimal point.
D.0.33; The student applied the rounding rule incorrectly.
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Frequently asked questions
What grade level is "Division with decimal quotients and rounding (Practice on workbooks)"?
Division with decimal quotients and rounding (Practice on workbooks) is a Grade 9 Mathematics lesson on ExcelOS.
What will I learn in Division with decimal quotients and rounding (Practice on workbooks)?
You'll be able to: Identify corresponding sides and angles in two congruent triangles given a diagram or a congruence statement, and justify their congruence using the definition of CPCTC (Corresponding Parts of Congruent Triangles are Congruent)….
Is "Division with decimal quotients and rounding (Practice on workbooks)" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Division with decimal quotients and rounding (Practice on workbooks)?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.