Learn on PengiPengi Math (Grade 8)Chapter 2: Exponents, Radicals, and Scientific Notation

Lesson 6: Operations with Scientific Notation

In this Grade 8 lesson from Pengi Math Chapter 2, students learn to perform all four operations — multiplication, division, addition, and subtraction — with numbers in scientific notation, including cases where exponents must be rewritten to match. Students apply exponent laws and practice converting results into proper scientific notation form where the coefficient satisfies 1 ≤ a < 10. The lesson also connects these skills to real-world contexts such as astronomical distances and atomic masses.

Section 1

Multiply and Divide in Scientific Notation

Property

To multiply and divide numbers in scientific notation, group the coefficients together and group the powers of 10 together, then use the Properties of Exponents.

  • Multiplication: Multiply the decimal coefficients and ADD the exponents.
(a×10m)(b×10n)=(a⋅b)×10m+n(a \times 10^m)(b \times 10^n) = (a \cdot b) \times 10^{m+n}
  • Division: Divide the decimal coefficients and SUBTRACT the exponents.
a×10mb×10n=(ab)×10m−n\frac{a \times 10^m}{b \times 10^n} = \left(\frac{a}{b}\right) \times 10^{m-n}

Section 2

Add Numbers in Scientific Notation with Same Powers

Property

When adding numbers in scientific notation with the same power of 10, use the distributive property:

(a×10n)+(b×10n)=(a+b)×10n(a \times 10^n) + (b \times 10^n) = (a + b) \times 10^n

Examples

Section 3

Subtract Numbers in Scientific Notation

Property

When subtracting numbers in scientific notation with the same power of 10, subtract the coefficients and keep the same power: (a×10n)−(b×10n)=(a−b)×10n(a \times 10^n) - (b \times 10^n) = (a - b) \times 10^n

Examples

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Chapter 2: Exponents, Radicals, and Scientific Notation

  1. Lesson 1

    Lesson 1: Integer Exponents and Properties

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  2. Lesson 2

    Lesson 2: Exponent Properties: Products, Quotients, and Powers

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  3. Lesson 3

    Lesson 3: Square Roots and Cube Roots

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  4. Lesson 4

    Lesson 4: Applications and Approximations of Square Roots

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  5. Lesson 5

    Lesson 5: Introduction to Scientific Notation

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  6. Lesson 6Current

    Lesson 6: Operations with Scientific Notation

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Section 1

Multiply and Divide in Scientific Notation

Property

To multiply and divide numbers in scientific notation, group the coefficients together and group the powers of 10 together, then use the Properties of Exponents.

  • Multiplication: Multiply the decimal coefficients and ADD the exponents.
(a×10m)(b×10n)=(a⋅b)×10m+n(a \times 10^m)(b \times 10^n) = (a \cdot b) \times 10^{m+n}
  • Division: Divide the decimal coefficients and SUBTRACT the exponents.
a×10mb×10n=(ab)×10m−n\frac{a \times 10^m}{b \times 10^n} = \left(\frac{a}{b}\right) \times 10^{m-n}

Section 2

Add Numbers in Scientific Notation with Same Powers

Property

When adding numbers in scientific notation with the same power of 10, use the distributive property:

(a×10n)+(b×10n)=(a+b)×10n(a \times 10^n) + (b \times 10^n) = (a + b) \times 10^n

Examples

Section 3

Subtract Numbers in Scientific Notation

Property

When subtracting numbers in scientific notation with the same power of 10, subtract the coefficients and keep the same power: (a×10n)−(b×10n)=(a−b)×10n(a \times 10^n) - (b \times 10^n) = (a - b) \times 10^n

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 2: Exponents, Radicals, and Scientific Notation

  1. Lesson 1

    Lesson 1: Integer Exponents and Properties

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  2. Lesson 2

    Lesson 2: Exponent Properties: Products, Quotients, and Powers

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  3. Lesson 3

    Lesson 3: Square Roots and Cube Roots

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  4. Lesson 4

    Lesson 4: Applications and Approximations of Square Roots

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  5. Lesson 5

    Lesson 5: Introduction to Scientific Notation

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  6. Lesson 6Current

    Lesson 6: Operations with Scientific Notation

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