Compare Decimals: Is 0.45 Equal to 0.445?

Q: Why isn't 0.45 the same as 0.445 if they're so close?

Close doesn't mean equal! The difference is $ 0.445 - 0.45 = 0.005 $, which may seem small but is still a real difference. In math, equal means exactly the same value.

Q: What's the easiest way to compare decimals like this?

Convert to fractions with the same denominator: $ \frac{45}{100} = \frac{450}{1000} $ and $ \frac{445}{1000} $. Now you can easily see that 450 ≠ 445!

Q: Do trailing zeros ever not matter?

Trailing zeros after the decimal point don't change value: 0.45 = 0.450 = 0.4500. But zeros that add new decimal places (like the 5 in 0.445) do create different values!

Q: Why did the explanation mention 45 vs 445?

It's showing the same pattern! Just like whole numbers 45 ≠ 445, decimals 0.45 ≠ 0.445. The extra digit makes them different values, whether in whole numbers or decimals.

Decimal Comparison with Trailing Zeros

$0.45\stackrel{?}{=}0.445$

Are the numbers above the same?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Are the numbers identical?

00:03 Let's convert from decimal to fraction, both 2 numbers

00:16 This number will have 1000 in the denominator due to the number of digits after the decimal point

00:23 It appears that the numbers are different

00:26 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

$0.45\stackrel{?}{=}0.445$

Are the numbers above the same?

Step-by-step solution

Just as the number 45 is not equal to 445, nor is the number 0.45 equal to 0.445—even though their values are relatively close.

This can be seen more clearly in the form of a regular fraction:

45/100 is not equal to 445/1000

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Trailing zeros change decimal value, not just appearance
Technique: Convert to fractions: 0.45 = 45/100, 0.445 = 445/1000
Check: Line up decimal points: 0.450 vs 0.445 shows difference ✓

Common Mistakes

Avoid these frequent errors

Thinking trailing zeros don't matter in decimal comparison
Don't ignore extra digits like the final 5 in 0.445 = wrong equality! This adds actual value (5/1000) making numbers unequal. Always compare each decimal place carefully from left to right.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Why isn't 0.45 the same as 0.445 if they're so close?

Close doesn't mean equal! The difference is $0.445 - 0.45 = 0.005$ , which may seem small but is still a real difference. In math, equal means exactly the same value.

How can I tell which decimal is bigger?

Line up the decimal points and compare digit by digit from left to right. Add zeros if needed: 0.450 vs 0.445. Since 5 > 4 in the thousandths place, 0.45 > 0.445.

What's the easiest way to compare decimals like this?

Convert to fractions with the same denominator: $\frac{45}{100} = \frac{450}{1000}$ and $\frac{445}{1000}$ . Now you can easily see that 450 ≠ 445!

Do trailing zeros ever not matter?

Trailing zeros after the decimal point don't change value: 0.45 = 0.450 = 0.4500. But zeros that add new decimal places (like the 5 in 0.445) do create different values!

Why did the explanation mention 45 vs 445?

It's showing the same pattern! Just like whole numbers 45 ≠ 445, decimals 0.45 ≠ 0.445. The extra digit makes them different values, whether in whole numbers or decimals.

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