Convert 89.65 to Fraction: Decimal Transformation Guide

Q: How do I know what denominator to use?

Count the decimal places! One decimal place = tenths (10), two decimal places = hundredths (100), three decimal places = thousandths (1000). Since 89.65 has 2 decimal places, use 100.

Q: Why isn't the answer simplified like 89 13/20?

Both forms are correct! $ 89\frac{65}{100} $ and $ 89\frac{13}{20} $ are the same value. The question asks for the conversion, so either unsimplified or simplified fractions work.

Q: What if the decimal has more places like 89.657?

Use the same method! Count decimal places: 89.657 has 3 decimal places, so write $ 89\frac{657}{1000} $. The rightmost digit determines your denominator.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to mixed fraction

00:03 Break down the number into whole number and remainder

00:06 Convert the remainder to a fraction

00:10 The denominator depends on the number of digits after the decimal point

00:16 There are 2 digits, so the denominator will be 100

00:23 Place the digits in the numerator as a number

00:26 Combine into a mixed fraction

00:32 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

Convert 89.65 into a fraction.

2

Step-by-step solution

Let's convert the decimal number 89.65 into a fraction step by step:

Step 1: Identify 89.65 as a mixed number with an integer part of 89 and a decimal part of 0.65.
Step 2: Express the decimal part 0.65 as a fraction:

0.65 can be written as $\frac{65}{100}$ because the digit 5 is in the hundredths place, meaning we divide 65 by 100.

Step 3: Combine the integer and fractional parts to form a mixed number:

The number 89.65 can be expressed as the mixed number $89 + \frac{65}{100}$ , or $89\frac{65}{100}$ .

Therefore, the decimal 89.65 can be expressed as $89\frac{65}{100}$ .

3

Final Answer

$89\frac{65}{100}$

Key Points to Remember

Essential concepts to master this topic

Rule: Count decimal places to determine the denominator power
Technique: 0.65 has 2 decimal places, so write $\frac{65}{100}$
Check: Verify $89\frac{65}{100} = 89.65$ by converting back ✓

Common Mistakes

Avoid these frequent errors

Using wrong denominator based on digit count
Don't count the digits in 65 and write $\frac{65}{10}$ = 95.5! This ignores decimal place value. Always use the rightmost decimal place: 2 places = hundredths = 100.

Practice Quiz

Test your knowledge with interactive questions

Convert into fraction form:

$$ 0.38= $$

FAQ

Everything you need to know about this question

How do I know what denominator to use?

+

Count the decimal places! One decimal place = tenths (10), two decimal places = hundredths (100), three decimal places = thousandths (1000). Since 89.65 has 2 decimal places, use 100.

Why isn't the answer simplified like 89 13/20?

+

Both forms are correct! $89\frac{65}{100}$ and $89\frac{13}{20}$ are the same value. The question asks for the conversion, so either unsimplified or simplified fractions work.

What if the decimal has more places like 89.657?

+

Use the same method! Count decimal places: 89.657 has 3 decimal places, so write $89\frac{657}{1000}$ . The rightmost digit determines your denominator.

Can I convert this to an improper fraction instead?

+

Yes! Multiply the whole number by the denominator, then add the numerator: $89 \times 100 + 65 = \frac{8965}{100}$ . Both mixed and improper forms are correct.

How do I check if my fraction equals the original decimal?

+

Divide the numerator by denominator and add the whole number: $65 \div 100 = 0.65$ , then $89 + 0.65 = 89.65$ ✓

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Convert 89.65 to Fraction: Decimal Transformation Guide

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