Percents & Decimals - Varsity Tutors

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Percents & Decimals

Study Guide

Key Definition

A percent is a way to express a number as a fraction of 100. A decimal is a number that represents a fraction using powers of 10.

Important Notes

  • To convert a percent to a decimal, divide by 100: $20\%$ becomes $0.2$
  • Decimals can represent fractions: $0.5$ is $\frac{1}{2}$
  • Percents are used to compare values easily since they are all out of 100
  • Decimals are useful for precision in calculations
  • Fractions, decimals, and percents are interconnected

Mathematical Notation

$\%$ represents a percent$\frac{a}{b}$ represents a fraction$\times$ or $*$ represents multiplication$\div$ or $/$ represents divisionRemember to use proper notation when solving problems

Why It Works

By converting between percents, decimals, and fractions, you can easily compare and compute with different types of numbers.

Remember

To convert a decimal to a percent, multiply by 100 and add the percent sign: $0.75$ becomes $75\%$

Quick Reference

Decimal to Percent:$\text{Decimal} \times 100 = \text{Percent}$Percent to Decimal:$\frac{\text{Percent}}{100} = \text{Decimal}$

Understanding Percents & Decimals

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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

INCOMPLETE: Replace this placeholder with a clear, beginner-level explanation (e.g., define percents and decimals, and show one worked example of each basic conversion).Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

Convert $25\%$ to a decimal.

A$0.25$B$0.025$C$2.5$D$0.0025$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

If you save $15\%$ of your allowance each week, how much do you save if your allowance is $\$50$?Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

Find the decimal equivalent of $\frac{3}{4}$.

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

Challenge Quiz

Single Choice QuizAdvanced

Convert $0.375$ to a percent.

A$37.5\%$B$3.75\%$C$375\%$D$0.375\%$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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