Compare Decimals: Finding the Relationship Between 2.16 and 2.150

Q: Why can I add zeros to the end of decimals?

Adding zeros to the right of a decimal doesn't change its value! For example, 2.16 = 2.160 = 2.1600. It's like saying 16 cents = 160 tenths of a cent.

Q: What if the numbers before the decimal are different?

Always compare the whole number part first! If they're different, that determines which is larger. Only compare decimal digits when the whole numbers are equal.

Q: Do I have to write out all the zeros?

Not in your final answer, but thinking about the zeros helps you compare correctly. $ 2.16 $ and $ 2.160 $ are the same number.

Q: What if all the decimal digits are the same?

Then the numbers are equal! For example, $ 3.40 = 3.4 $ because when we align them as 3.40 and 3.40, every digit matches.

Decimal Comparison with Trailing Zeros

Fill in the missing sign:

$2.16\text{ }_{—\text{ }}2.150$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the appropriate sign

00:04 Let's compare the digits between the numbers

00:13 6 is greater than 5 therefore this number is bigger

00:17 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the missing sign:

$2.16\text{ }_{—\text{ }}2.150$

Step-by-step solution

In order to compare which is larger, we will compare the numbers by adding 0 to 2.16 in the following way:

$2.160?2.150$

Note that before the decimal point we have 2 in both numbers

After the decimal point in both numbers we have 1

The different numbers are the ones that follow, 6 versus 5

Since 6 is greater than 5, the appropriate sign is:

$2.160 > 2.150$

Final Answer

$>$

Key Points to Remember

Essential concepts to master this topic

Rule: Add zeros to match decimal places before comparing
Technique: Convert 2.16 to 2.160 to compare with 2.150
Check: Compare digit by digit: 2=2, 1=1, 6>5, so 2.16>2.150 ✓

Common Mistakes

Avoid these frequent errors

Comparing decimals without aligning decimal places
Don't just compare 16 vs 150 thinking 150 is bigger = wrong answer! This ignores place value completely. Always align decimal places by adding zeros, then compare digit by digit from left to right.

Practice Quiz

Test your knowledge with interactive questions

Reduce the following fraction:

$$ 0.30 $$

FAQ

Everything you need to know about this question

Why can I add zeros to the end of decimals?

Adding zeros to the right of a decimal doesn't change its value! For example, 2.16 = 2.160 = 2.1600. It's like saying 16 cents = 160 tenths of a cent.

What if the numbers before the decimal are different?

Always compare the whole number part first! If they're different, that determines which is larger. Only compare decimal digits when the whole numbers are equal.

Do I have to write out all the zeros?

Not in your final answer, but thinking about the zeros helps you compare correctly. $2.16$ and $2.160$ are the same number.

How do I compare more than two decimal places?

Use the same method! Add zeros to make all decimals have the same number of places, then compare digit by digit from left to right until you find a difference.

What if all the decimal digits are the same?

Then the numbers are equal! For example, $3.40 = 3.4$ because when we align them as 3.40 and 3.40, every digit matches.

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