Compare 230/100 and 2.3: Choosing the Correct Mathematical Symbol

Decimal Comparison with Fraction Conversion

Choose the appropriate sign (?):

230100?2.3 \frac{230}{100}?2.3

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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 Convert a fraction to a decimal fraction
00:07 Place the numerator as a whole number
00:11 When the denominator equals 100, move the decimal point 2 places left
00:19 Place the decimal fraction instead of the fraction
00:24 Select the appropriate sign
00:28 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Choose the appropriate sign (?):

230100?2.3 \frac{230}{100}?2.3

2

Step-by-step solution

We begin by converting 230100\frac{230}{100} into a decimal form. To do this, we divide 230 by 100:

230100=230÷100=2.3 \frac{230}{100} = 230 \div 100 = 2.3

Now, we compare this result to the given decimal 2.3.

Since 2.3=2.32.3 = 2.3, the appropriate sign to use between 230100\frac{230}{100} and 2.3 is "=""=".

Therefore, the solution to the problem is =\mathbf{=}.

3

Final Answer

=

Key Points to Remember

Essential concepts to master this topic
  • Rule: Convert fractions to decimals by dividing numerator by denominator
  • Technique: 230100=230÷100=2.3 \frac{230}{100} = 230 \div 100 = 2.3
  • Check: Compare converted values: 2.3 = 2.3 shows equality ✓

Common Mistakes

Avoid these frequent errors
  • Comparing fraction and decimal without converting
    Don't try to compare 230100 \frac{230}{100} directly to 2.3 without converting = confusion and wrong answers! The fraction form looks bigger than the decimal. Always convert to the same form first, then compare the values.

Practice Quiz

Test your knowledge with interactive questions

Write the following fraction as a decimal:

\( \frac{5}{100}= \)

FAQ

Everything you need to know about this question

Why do I need to convert the fraction to a decimal?

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Converting to the same format makes comparison much easier! When you see 230100 \frac{230}{100} vs 2.3, it's hard to tell they're equal until both are in decimal form.

Can I convert the decimal to a fraction instead?

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Yes! You could write 2.3 as 2310 \frac{23}{10} or 230100 \frac{230}{100} . Both methods work, but decimal conversion is usually faster for this type of problem.

How do I divide 230 by 100 quickly?

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When dividing by 100, just move the decimal point 2 places left! So 230 becomes 2.30 or simply 2.3. This works because 100 = 10².

What if the numbers don't come out equal?

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Then you'd use < or > symbols! Convert both to decimals first, then compare digit by digit from left to right to determine which is larger or smaller.

Do I always get a nice decimal when dividing?

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Not always! Some fractions like 13 \frac{1}{3} give repeating decimals (0.333...). But fractions with denominators of 10, 100, 1000 usually give terminating decimals.

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