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Grade 7:  The Learning Equation Math

11.02 Expanded Notation and Decimals

Number Concepts

Refresher pp 4-5

Key Objectives:

The student will:

Whole Number Expanded Numeral Expanded Numeral using Powers of 10
5 5 x 1 5 x 10o
56 5 x 10 + 6 x 1 5 x 101 + 6 x 10o
567 5 x 100 + 6 x 10 + 7 x 1 5 x 102 + 6 x 101 + 7 x 10o
5678 5 x 1000 + 6 x 100 + 7 x 10 + 8 x 1 5 x 103 + 6 x 102 + 7 x 101 + 8 x 10o

 

Standard Form Expanded Form (Powers of 10) Word Form
5.4 5 x 10o + 4 x 0.1 five and four tenths
56.25 5 x 101 + 6 x 10o + 2 x 0.1 + 5 x 0.01 fifty-six and twenty-five hundredths
956.7 9 x 102 + 5 x 101 + 6 x 10o + 7 x 0.1 nine hundred fifty-six and seven tenths
456.789 4x102 + 5x101 + 6x10o + 7x0.1 + 8x0.01 + 9x0.001 four hundred fifty-six and seven hundred eighty-nine thousandths

 

Standard Name Abacus Representation Expanded Numeral using Powers of 10

3424

The number: 87,654,321 on the Abacus

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3 x 103 + 4 x 102 + 6 x 101 + 2 x 100

123 456

The number: 87,654,321 on the Abacus

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1 x 105 + 2 x 104 + 3 x 103 + 4 x 102 + 5 x 101 + 6 x 100
source:  The Abacus: Introduction

 

Expanded Form to Standard Name

Quia - Matching - Read That Number!

 

Review:

Term Example(s) Explanation
standard form 5, 255, 3459

The standard form is the normal symbol we write for a number

exponent

 23, 34, 46, 54, 65 the exponent is the number of times the base is multiplied by itself
base the base is the number being multiplied
power 54 the result of multiplying a number by itself one or more times
power of 10 101, 102, 103, 104 the base of the power is 10
coefficient 4 x 103

15 x 42

 the number before the times sign in a term where a number is being multiplied by a power
expanded numeral 5 x 10

2 x 100 + 5 x 10 + 5 x 1

3 x 1000 + 4 x 100 + 5 x 10 + 9 x 1

 The expanded form shows the value of each digit of a number in standard form.
expanded numeral powers of 10 5 x 10o

2 x 102 + 5 x 101 + 5 x 10o

3 x 103 + 4 x 102 + 5 x 101 + 9 x 10o

 The expanded form shows the value of each digit of a number in standard form using a power of 10.

Base 10 Blocks: Exploring Whole Decimal Numbers with Blocks

Word Form

 

Enrichment:

 

standard form, expanded form, coefficient, power of 10, exponent

Prerequisite Skills:

Place Value!

Estimating the Sum

 

Powers and Exponents:  Grade 7 Lesson 11.01

 
 

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