Learn on PengiBig Ideas Math, Course 2, AcceleratedChapter 6: Exponents and Scientific Notation

Lesson 6: Writing Scientific Notation

In this Grade 7 lesson from Big Ideas Math, Course 2, Accelerated, students learn how to convert numbers into scientific notation by moving the decimal point and applying positive or negative exponents of powers of 10. The lesson covers writing both large numbers and small decimals in the form a × 10^n, using real-world examples such as large financial figures and microscopic measurements. Students practice identifying when to use positive versus negative exponents based on whether the original number is greater than or less than 1.

Section 1

Convert to Scientific Notation

Property

A number is in scientific notation if it is expressed as the product of a number between 1 and 10 and a power of 10.

To Write a Number in Scientific Notation.

  1. Locate the decimal point so that there is exactly one nonzero digit to its left.
  2. Count the number of places you moved the decimal point: this determines the power of 10.

a. If the original number is greater than 10, the exponent is positive.
b. If the original number is less than 1, the exponent is negative.

Examples

  • To write a large number in scientific notation: 475,000,000=4.75×108475,000,000 = 4.75 \times 10^8.
  • To write a small number in scientific notation: 0.000082=8.2×10−50.000082 = 8.2 \times 10^{-5}.
  • To perform a calculation: 9.6×1083×103=(9.63)×108−3=3.2×105\frac{9.6 \times 10^8}{3 \times 10^3} = (\frac{9.6}{3}) \times 10^{8-3} = 3.2 \times 10^5.

Section 2

Scientific Notation with a Zero Exponent

Property

For any number cc such that 1≤c<101 \leq c < 10, the scientific notation is given by the formula:

c=c×100c = c \times 10^0

Examples

Section 3

Real-World Applications of Scientific Notation

Property

Scientific notation is a practical tool used in many fields to express and compare very large or very small measurements. The same procedure for converting standard numbers applies to real-world quantities, providing a compact and standardized way to represent data.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Convert to Scientific Notation

Property

A number is in scientific notation if it is expressed as the product of a number between 1 and 10 and a power of 10.

To Write a Number in Scientific Notation.

  1. Locate the decimal point so that there is exactly one nonzero digit to its left.
  2. Count the number of places you moved the decimal point: this determines the power of 10.

a. If the original number is greater than 10, the exponent is positive.
b. If the original number is less than 1, the exponent is negative.

Examples

  • To write a large number in scientific notation: 475,000,000=4.75×108475,000,000 = 4.75 \times 10^8.
  • To write a small number in scientific notation: 0.000082=8.2×10−50.000082 = 8.2 \times 10^{-5}.
  • To perform a calculation: 9.6×1083×103=(9.63)×108−3=3.2×105\frac{9.6 \times 10^8}{3 \times 10^3} = (\frac{9.6}{3}) \times 10^{8-3} = 3.2 \times 10^5.

Section 2

Scientific Notation with a Zero Exponent

Property

For any number cc such that 1≤c<101 \leq c < 10, the scientific notation is given by the formula:

c=c×100c = c \times 10^0

Examples

Section 3

Real-World Applications of Scientific Notation

Property

Scientific notation is a practical tool used in many fields to express and compare very large or very small measurements. The same procedure for converting standard numbers applies to real-world quantities, providing a compact and standardized way to represent data.

Examples