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Comparing Decimals

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Comparing Decimals

Study Guide

Key Definition

We compare decimals by first checking the whole numbers (integer part) and then looking at the decimal part (fraction part). If the decimals have different number of places, we can add zeros to the shorter decimal to make them equal in length.

Important Notes

The number with the larger integer part is the greater number.
If the integer parts are the same, the number with the greater decimal part is the larger number.
When the decimal parts have different number of places, add zeros to the shorter decimal to make them equal in length.

Mathematical Notation

$a.b$ represents a decimal number where $a$ is the integer part and $b$ is the decimal part.

Remember to align the decimal points when comparing decimal numbers.

Why It Works

This works because of the place value system. Each digit in a number has a value based on its position. The integer part is based on powers of 10, while the decimal part is based on fractions of 10.

Remember

Always align the decimal points and compare the digits from left to right.

Quick Reference

Decimal Number:$\text{Integer Part . Decimal Part}$

Understanding Comparing Decimals

Choose your learning level

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Two decimals are compared by checking the integer part first, then the decimal part. If needed, we add zeroes to the shorter decimal to make them of equal length.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which is greater, $7.8$ or $7.099$?

Real-World Problem

Question Exercise

Intermediate

Shopping Scenario

You are shopping and see two deals for a bag of oranges. One store sells it for $$7.8$ per bag and another store sells it for $$7.099$ per bag. Which store offers the cheaper deal?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Arrange the numbers $7.8$, $7.099$, and $7.8$ in ascending order.

Challenge Quiz

Single Choice Quiz

Advanced

Which is smaller, $0.09$ or $0.009$?

Recap

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Review key concepts and takeaways