Mathematics
Grade 10
15 min
Convert between decimals and fractions or mixed numbers
Convert between decimals and fractions or mixed numbers
What you'll learn
- Apply the rules of arithmetic operations to accurately add, subtract, multiply, and divide complex numbers expressed in standard form (a + bi).
- Solve complex number equations involving addition, subtraction, multiplication, and division, and express the solutions in simplified a + bi form.
- Explain the geometric interpretation of complex number addition and subtraction using the complex plane and vector representation.
- Identify and correct errors in complex number arithmetic, justifying each step with appropriate properties and definitions.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Convert any terminating decimal into a simplified fraction or mixed number.
Convert any fraction or mixed number into its exact decimal equivalent, identifying it as terminating or repeating.
Analyze the prime factors of a fraction's denominator to predict whether its decimal form will terminate or repeat.
Convert simple repeating decimals (e.g., 0.555...) into simplified fractions using an algebraic method.
Convert complex repeating decimals (e.g., 0.12333...) into simplified fractions using an algebraic method.
Apply conversion skills to solve multi-step problems that involve both decimal and fractional representations of numbers.
Ever tried to split a $25.50 bill three ways, or measure exactly 5/16 of an inch for a project? 🤔 Understanding how to...
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Key Concepts & Vocabulary
TermDefinitionExample
Terminating DecimalA decimal number that has a finite number of digits after the decimal point.0.625 is a terminating decimal because it ends after the digit 5.
Repeating DecimalA decimal number that has a digit or a block of digits that repeats infinitely after the decimal point. The repeating block is called the period.0.454545... is a repeating decimal with a period of '45'. It can be written as 0.\overline{45} using a vinculum.
Rational NumberAny number that can be expressed as a quotient or fraction p/q of two integers, where p is the numerator and q is the non-zero denominator.Both 0.75 (which is 3/4) and 0.\overline{3} (which is 1/3) are rational numbers.
Mixed NumberA number composed of a whole number and a proper fraction.4 3/8 is a mixed number, r...
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Core Formulas
Terminating Decimal to Fraction
x = \frac{\text{digits after decimal}}{\text{10}^{\text{n}}}
To convert a terminating decimal to a fraction, write the digits after the decimal point as the numerator. The denominator is 10 raised to the power of 'n', where 'n' is the number of decimal places. Always simplify the resulting fraction.
Fraction to Decimal
\frac{a}{b} = a \div b
To convert a fraction to a decimal, perform long division of the numerator by the denominator. The result will either terminate or enter a repeating pattern.
Algebraic Conversion of Repeating Decimals
1. \text{Let } x = \text{the repeating decimal.} \newline 2. \text{Create two equations by multiplying } x \text{ by powers of 10 to shift the decimal point.} \newline 3. \text{Subtr...
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Challenging
The repeating decimal 0.0ababab... (where 'a' and 'b' are digits) is converted to a fraction. Which expression represents this fraction before any simplification?
A.ab/99
B.ab/100
C.ab/990
D.ab/999
Challenging
A plank of wood is 4.2 meters long. It is to be cut into smaller pieces, each exactly 3/8 of a meter long. How many full pieces can be cut, and what is the length of the remaining piece, expressed as a simplified fraction of a meter?
A.11 pieces, 3/40 m remaining
B.11 pieces, 1/5 m remaining
C.12 pieces, 1/10 m remaining
D.10 pieces, 1/4 m remaining
Challenging
The fraction 7/(2ⁿ * 5ᵐ * k) is in its simplest form, where n and m are non-negative integers. For the fraction to be equivalent to a terminating decimal, what must be true about the integer k?
A.k must be a prime number.
B.k must be equal to 1.
C.k must be a factor of 7.
D.k must be an even number.
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Frequently asked questions
What grade level is "Convert between decimals and fractions or mixed numbers"?
Convert between decimals and fractions or mixed numbers is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Convert between decimals and fractions or mixed numbers?
You'll be able to: Apply the rules of arithmetic operations to accurately add, subtract, multiply, and divide complex numbers expressed in standard form (a + bi); Solve complex number equations involving addition, subtraction, multiplication, and….
Is "Convert between decimals and fractions or mixed numbers" 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 Convert between decimals and fractions or mixed numbers?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.