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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 the number of tenths, e.g., $0.3 = \frac{3}{10}$
The second digit indicates the number of hundredths, e.g., $3.26 = 3 \frac{26}{100}$
Use base 10 blocks to visualize decimal places
Decimals can represent both fractions and mixed numbers
Each place value is a power of 10

Mathematical Notation

$\frac{a}{b}$ means a divided by b

$+$ represents addition

$-$ represents subtraction

$\times$ represents multiplication

$\div$ represents division

$.$ is the decimal point, separating integer and fractional parts

Remember to use proper notation when solving problems

Why It Works

Decimals simplify the representation of fractions and mixed numbers, making calculations easier with powers of 10.

Remember

Each digit in a decimal has a specific place value, based on powers of 10, such as tenths, hundredths, thousandths, etc.

Quick Reference

Tenths:$0.1 = \frac{1}{10}$

Hundredths:$0.01 = \frac{1}{100}$

Thousandths:$0.001 = \frac{1}{1000}$

Understanding Place Value: Decimals

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Video explanation of this concept

Beginner

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Beginner Explanation

Decimals use digits to the right of a decimal point to represent fractions. For example, in 0.5, the 5 is in the tenths place and means five tenths (5/10). In 0.75, the 7 is in the tenths place (7/10) and the 5 is in the hundredths place (5/100).

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the decimal representation of $\frac{7}{10}$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have $\$3.26$ and spend $\$1.50$. How much money do you have left?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

What fraction is equivalent to the decimal $0.125$?

Challenge Quiz

Single Choice Quiz

Advanced

What is the decimal representation of $\frac{123}{1000}$?

Recap

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Review key concepts and takeaways