Mathematics
Grade 10
15 min
Convert decimals between standard and expanded form using fractions
Convert decimals between standard and expanded form using fractions
What you'll learn
- Identify the place value of each digit in a decimal number to the hundredths place.
- Explain how to write a decimal number (up to the hundredths place) as a fraction with a denominator of 10 or 100.
- Convert decimals (up to the hundredths place) from standard form to expanded form using fractions with denominators of 10 and 100.
- Convert decimals (up to the hundredths place) from expanded form (using fractions with denominators of 10 and 100) back to standard form.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Logically deconstruct any decimal number into its constituent parts using fractional place values.
Write the expanded form of a decimal using fractions by identifying the place value of each digit.
Convert a decimal from its expanded fractional form back into its compact standard form.
Justify the value of a decimal by expressing it as a logical sum of its parts.
Analyze and correct errors in decimal conversions by applying the rules of place value logic.
Articulate the relationship between a digit's position and its value, represented as a fraction with a power of 10 in the denominator.
Is the number 45.03 the same as (4 * 10) + (5 * 1) + (3 * 1/10)? Let's use logic to find out! 🤔
This tutorial explores the logical structure of the decimal sy...
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Key Concepts & Vocabulary
TermDefinitionExample
Standard FormThe conventional, compact way of writing a number using digits, where the position of each digit determines its value.The number 52.309 is in standard form.
Expanded FormA logical representation of a number as a sum of its digits, each multiplied by its corresponding place value. In this context, the place values for the decimal part are expressed as fractions.The expanded form of 52.309 is (5 * 10) + (2 * 1) + (3 * 1/10) + (0 * 1/100) + (9 * 1/1000).
Place ValueThe value of a digit based on its position relative to the decimal point. Each place is a power of 10.In 52.309, the '3' is in the tenths place, so its value is 3/10.
Decimal PointA symbol that logically separates the whole number part from the fractional part of a number.In 52.309, the...
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Core Formulas
Standard to Expanded Form Conversion
For a number N with digits ...d₂d₁d₀.d₋₁d₋₂d₋₃..., its expanded form is: N = ... + (d₂ * 10²) + (d₁ * 10¹) + (d₀ * 10⁰) + (d₋₁ * 1/10¹) + (d₋₂ * 1/10²) + (d₋₃ * 1/10³)...
This rule provides the logical structure for deconstructing a number. Identify each digit and its place value (represented as 10, 1, 1/10, 1/100, etc.) and write the number as a sum of these products.
Expanded to Standard Form Conversion
Given an expanded form Σ(dᵢ * 10ⁱ), where i is an integer, construct the standard form by placing each digit dᵢ in the position corresponding to the power i.
This rule is for synthesis. Evaluate each term to identify the digit and its place value. Then, assemble the digits in the correct order around a decimal point, using zeros as place...
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Challenging
A number N is constructed using the following logical rules: The digit in the 10¹ place is 2. The digit in the 10⁻² place is twice the digit in the 10¹ place. The digit in the 10⁰ place is 3. The digit in the 10⁻³ place is one greater than the digit in the 10¹ place. All other digits are 0. What is N?
A.23.023
B.23.043
C.23.403
D.32.043
Challenging
Consider the decimal D = 0.abc, where a, b, and c are non-zero digits. Which expression is logically equivalent to D?
A.(a * 1/10) + (b * 1/100) + (c * 1/1000)
B.(a * 100/1000) + (b * 10/1000) + (c * 1/1000)
C.(100a + 10b + c) / 1000
D.All of the above
Challenging
A logical proof aims to demonstrate that 0.7 is equivalent to 0.70. Which key concept is central to this proof?
A.The value of 0.7 is (7 * 1/10), while the value of 0.70 is (7 * 1/10) + (0 * 1/100). Since adding zero does not change the value, they are equivalent.
B.Both numbers have the same first digit, so they must be equivalent.
C.Removing a zero from the end of a decimal does not change its value, which is a fundamental axiom of mathematics.
D.The standard form is a more compact representation, but the expanded form is more precise, proving 0.70 is larger.
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What grade level is "Convert decimals between standard and expanded form using fractions"?
Convert decimals between standard and expanded form using fractions is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Convert decimals between standard and expanded form using fractions?
You'll be able to: Identify the place value of each digit in a decimal number to the hundredths place; Explain how to write a decimal number (up to the hundredths place) as a fraction with a denominator of 10 or 100; Convert decimals (up to the….
Is "Convert decimals between standard and expanded form using fractions" 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 decimals between standard and expanded form using fractions?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.