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Place Value: Decimals

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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 multiplication

A decimal point "." separates the whole-number part from the fractional part

Remember 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

Choose your learning level

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Video explanation of this concept

Beginner

Start here! Easy to understand

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.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

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

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have $0.75$ of a pizza left. How would you express this as a fraction?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Convert the decimal $0.125$ to a fraction.

Challenge Quiz

Single Choice Quiz

Advanced

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

Recap

Watch & Learn

Review key concepts and takeaways