Compare Decimals: Find the Inequality Symbol Between 1.33 and 1.333

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

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

Q: How do I remember which symbol means what?

Think of the symbols as arrows: $ points to the smaller number, and \( > $ points to the smaller number. The wide end always faces the bigger number!

Q: What if I get confused with place values?

Write the decimal places above each digit: tenths, hundredths, thousandths. Compare from left to right, just like reading. The first different digit tells you which decimal is larger.

Q: Can decimals ever be equal even if they look different?

Yes! 0.5 = 0.50 = 0.500 because trailing zeros don't change the value. But be careful - $ 1.33 \neq 1.333 $ because the digits are actually different.

Decimal Comparison with Place Value Analysis

Fill in the missing sign:

$1.33\text{ }_{—\text{ }}1.333$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the appropriate sign

00:03 Let's compare the digits between the numbers

00:18 3 is greater than 0 so this number is larger

00:21 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:

$1.33\text{ }_{—\text{ }}1.333$

Step-by-step solution

In order to compare which is larger, we will compare the numbers by adding 0 to 1.33 as follows:

$1.330\text{?}1.333$

Note that before the decimal point we have 1 in both numbers

After the decimal point in both numbers we have the number 3 and then the number 3

The different numbers are the last numbers 0 versus 3

Since 3 is greater than 0 the appropriate sign is:

$1.330 < 1.333$

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Rule: Compare decimals digit by digit from left to right
Technique: Add zeros to make equal places: 1.33 becomes 1.330
Check: Compare thousandths place: 0 < 3, so 1.330 < 1.333 ✓

Common Mistakes

Avoid these frequent errors

Comparing decimal length instead of value
Don't think 1.333 is bigger just because it has more digits = wrong comparison! More digits doesn't always mean larger value (0.1 > 0.09). Always align decimal places and 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 after the last digit doesn't change the value! 1.33 = 1.330 = 1.3300 - they're all exactly the same number. This helps us compare more easily.

What if the numbers before the decimal point are different?

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

How do I remember which symbol means what?

Think of the symbols as arrows: $<$ points to the smaller number, and $>$ points to the smaller number. The wide end always faces the bigger number!

What if I get confused with place values?

Write the decimal places above each digit: tenths, hundredths, thousandths. Compare from left to right, just like reading. The first different digit tells you which decimal is larger.

Can decimals ever be equal even if they look different?

Yes! 0.5 = 0.50 = 0.500 because trailing zeros don't change the value. But be careful - $1.33 \neq 1.333$ because the digits are actually different.

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