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What Does the Fourth Decimal Place Tell Us?

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The World of Numbers · Chapter challenge problems · 3:38

You'll learn: Relate a last non-zero fourth decimal digit to a numerator over 10⁴ and examine reduction.

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What Does the Fourth Decimal Place Tell Us?

3:38

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What Does the Fourth Decimal Place Tell Us?

You'll learn: Relate a last non-zero fourth decimal digit to a numerator over 10⁴ and examine reduction.

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Same topic

Chapter challenge problems

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Find More Reciprocals with Cyclic Repeating Blocks
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Find More Reciprocals with Cyclic Repeating Blocks
You'll learn: Test reciprocal decimals and compare rotations of their repeating blocks.
Make Enough Space Between Fraction Numerators
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Make Enough Space Between Fraction Numerators
You'll learn: Choose an equivalent common denominator with enough integer numerator positions between two fractions.
Can Three Rational Numbers Satisfy Both Zero Conditions?
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Can Three Rational Numbers Satisfy Both Zero Conditions?
You'll learn: Combine the sum and pairwise-product conditions to obtain a sum of squares equal to zero.
Prove That the Average Really Lies Between Two Numbers
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Prove That the Average Really Lies Between Two Numbers
You'll learn: Justify both rationality of the average and its strict location between distinct endpoints.

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Understanding and proving identities

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Three Consecutive Squares Always Give Two
3:21
Three Consecutive Squares Always Give Two
You'll learn: Explore the opening square-number calculation and formulate the observed pattern.
An Identity Is an Equation True for Every Allowed Value
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An Identity Is an Equation True for Every Allowed Value
You'll learn: Distinguish an identity from an equation holding only for certain inputs.
Build the Square of a Sum from Four Pieces
3:13
Build the Square of a Sum from Four Pieces
You'll learn: Partition a square of side a+b into a², b² and two ab rectangles.
Why the Square Identity Also Works for Negative Numbers
3:20
Why the Square Identity Also Works for Negative Numbers
You'll learn: Move from area pictures to a distributive proof valid for signed and rational values.
When Is the Square of a Sum Bigger Than the Sum of Squares?
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When Is the Square of a Sum Bigger Than the Sum of Squares?
You'll learn: Use the sign of 2ab to compare (a+b)² with a²+b².
Square a Binomial with Coefficients and Fractions
3:30
Square a Binomial with Coefficients and Fractions
You'll learn: Identify the complete expressions playing the roles of a and b and expand correctly.
Use Nearby Round Numbers to Calculate Squares
3:25
Use Nearby Round Numbers to Calculate Squares
You'll learn: Choose a convenient additive split and evaluate with (a+b)².

Next topic

Perfect-square factorisation

4

Read a Perfect Square Backwards
3:27
Read a Perfect Square Backwards
You'll learn: Recognise a²+2ab+b² and write its repeated factor.
Take Out a Common Factor Before Looking for a Square
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Take Out a Common Factor Before Looking for a Square
You'll learn: Extract a common factor to expose a simpler perfect-square expression.
Derive the Square of a Difference by Substitution
3:19
Derive the Square of a Difference by Substitution
You'll learn: Replace b with −b in the square-of-a-sum identity.
See the Square of a Difference as an Area
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See the Square of a Difference as an Area
You'll learn: Remove the two appropriate rectangles from the larger square.