Compare Decimals: Is 0.45 Equal to 0.045?

Decimal Comparison with Place Value Differences

Are the fractions equal?

0.45=?0.045 0.45 \stackrel{?}{=} 0.045

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Step-by-step written solution

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1

Understand the problem

Are the fractions equal?

0.45=?0.045 0.45 \stackrel{?}{=} 0.045

2

Step-by-step solution

To determine if these two decimal fractions are equal, we compare the numbers directly. The first number is 0.45 0.45 , which is equivalent to the fraction 45100 \frac{45}{100} . The second number is 0.045 0.045 , which is equivalent to the fraction 451000 \frac{45}{1000} .

First, let's convert 0.45 0.45 to thousandths to compare it directly with 0.045 0.045 :

0.45=45100=4501000 0.45 = \frac{45}{100} = \frac{450}{1000}

Now, compare 4501000 \frac{450}{1000} and 451000 \frac{45}{1000} : clearly, 450≠45 450 \neq 45 .

Therefore, 0.45≠0.045 0.45 \neq 0.045 , making the expression false.

3

Final Answer

≠ \neq

Key Points to Remember

Essential concepts to master this topic
  • Place Value: Each decimal position represents a different power of ten
  • Technique: Convert to same denominator: 0.45 = 450/1000, 0.045 = 45/1000
  • Check: Compare numerators when denominators match: 450 ≠ 45 ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring decimal place positions
    Don't think 0.45 and 0.045 are the same because they both have '45' = completely wrong values! The decimal positions matter enormously - 0.45 is ten times larger than 0.045. Always count decimal places carefully to determine true value.

Practice Quiz

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Which decimal number is greater?

FAQ

Everything you need to know about this question

Why aren't 0.45 and 0.045 equal if they both have 45?

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The position of digits matters! 0.45 0.45 means 45 hundredths, while 0.045 0.045 means 45 thousandths. That's like comparing 45 cents to 4.5 cents!

How can I easily compare decimals with different lengths?

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Add zeros to make them the same length: 0.45=0.450 0.45 = 0.450 . Now compare digit by digit: 0.450 vs 0.045. Clearly 450 thousandths is much larger than 45 thousandths!

What's the fastest way to see which decimal is bigger?

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Look at the first non-zero digit after the decimal point. In 0.45, it's in the tenths place (4). In 0.045, it's in the hundredths place (4). The tenths place is always larger!

Can I convert to fractions to compare?

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Absolutely! 0.45=45100 0.45 = \frac{45}{100} and 0.045=451000 0.045 = \frac{45}{1000} . Since 45100=4501000 \frac{45}{100} = \frac{450}{1000} , you can clearly see 450 > 45.

Does the number of decimal places tell me anything?

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Yes! More decimal places usually mean smaller numbers (when the leading digits are the same). 0.045 has 3 decimal places vs 0.45 with 2, so 0.045 is the smaller number.

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