Scientific Notation - Varsity Tutors

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Scientific Notation

Study Guide

Key Definition

Scientific notation is a way to express very large or very small numbers more simply, as the product of a number between $1$ and $10$ and a power of 10.

Important Notes

  • When a positive number greater than or equal to $10$ is written in scientific notation, the power of 10 used is positive.
  • When the number is less than $1$, the power of 10 used is negative.
  • The exponent in scientific notation indicates the number of places the decimal point is moved.
  • Positive powers of 10 indicate large numbers.
  • Negative powers of 10 indicate small numbers.

Mathematical Notation

$10^n$ means move the decimal point $n$ places to the right$10^{-n}$ means move the decimal point $n$ places to the leftRemember to use proper notation when solving problems

Why It Works

Scientific notation simplifies calculations with very large or very small numbers by reducing the number of digits you need to work with, using powers of 10.

Remember

Always express the number part of scientific notation as $a \times 10^n$, where $1 \leq a < 10$

Quick Reference

Positive Powers:$10^1 = 10$, $10^2 = 100$, $10^3 = 1000$Negative Powers:$10^{-1} = 0.1$, $10^{-2} = 0.01$, $10^{-3} = 0.001$

Understanding Scientific Notation

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Video explanation of this concept

concept. Use space or enter to play video.concept thumbnailBeginner

Start here! Easy to understand

BeginnerIntermediateAdvanced

Beginner Explanation

Scientific notation makes it easier to handle very large or small numbers by using powers of 10.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

Which of the following is the correct scientific notation for 5000?

A$5 \times 10^3$B$0.5 \times 10^4$C$5 \times 10^2$D$50 \times 10^2$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

A teen is saving for a new gaming console. The console costs 300,000 cents. Express this amount in scientific notation.Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

Express the number 0.000076 in scientific notation.

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

Which of the following represents the number 0.000000456 in scientific notation?

A$4.56 \times 10^{-7}$B$4.56 \times 10^{-8}$C$45.6 \times 10^{-8}$D$0.456 \times 10^{-6}$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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Review key concepts and takeaways

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