Place Value: Decimals - Varsity Tutors

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Place Value: Decimals

Study Guide

Key Definition

Decimals are a shorthand way to write fractions and mixed numbers with denominators that are powers of 10, like $10$, $100$, $1000$, etc.

Important Notes

  • The first digit to the right of the decimal point indicates tenths: $0.3 = \frac{3}{10}$
  • The second digit to the right of the decimal point indicates hundredths: $3.26 = 3 \frac{26}{100}$
  • Decimals can have many places to the right: $51.48053 = 51 \frac{48053}{100000}$
  • Use base 10 blocks to visualize decimals effectively
  • The first digit to the left of the decimal point is the ones digit

Mathematical Notation

$\frac{a}{b}$ represents a fraction$+$ represents addition$\cdot$ represents multiplicationA decimal point "." separates the whole-number part from the fractional partRemember to use proper notation when solving problems

Why It Works

Decimals efficiently represent fractions and mixed numbers by using powers of 10 in their denominators, making calculations easier.

Remember

Visualize decimals with base 10 blocks: one large square represents one whole, strips represent tenths, and smaller squares represent hundredths.

Quick Reference

Tenths:$0.1$Hundredths:$0.01$

Understanding Place Value: Decimals

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Video explanation of this concept

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

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Beginner Explanation

Every position in a decimal has a value. The first place to the right of the decimal point is tenths (1/10); the next is hundredths (1/100). For example, 0.7 means 7 tenths, and 0.05 means 5 hundredths.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

Which decimal is equivalent to $\frac{3}{10}$?

A$0.3$B$0.03$C$3.0$D$0.33$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

You have $0.75$ of a pizza left. How would you express this as a fraction?Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

Convert the decimal $0.125$ to a fraction.

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

Challenge Quiz

Single Choice QuizAdvanced

Which decimal represents $\frac{26}{100}$?

A$0.26$B$2.6$C$0.026$D$26.0$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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