Convert Decimal 0.708 to Fraction: Step-by-Step Solution

Q: How do I know what denominator to use?

Count the decimal places! One place = 10, two places = 100, three places = 1000. Since 0.708 has three decimal places, use 1000 as your denominator.

Q: Should I simplify the fraction after converting?

The question asks for the conversion, so $ \frac{708}{1000} $ is the correct answer. You could simplify it to $ \frac{177}{250} $, but that's not required here.

Q: What if the decimal has zeros at the end?

Still count all decimal places! For example, 0.750 has three decimal places, so it becomes $ \frac{750}{1000} $, even though the last digit is zero.

Q: Why can't I use 100 as the denominator for 0.708?

Because 0.708 goes to the thousandths place, not the hundredths place. Using 100 would give you $ \frac{708}{100} $ = 7.08, which is wrong!

Decimal to Fraction with Place Value

Convert 0.708 into a fraction.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to a simple fraction

00:03 Move the decimal point right until the number is whole

00:06 In a decimal fraction, the denominator is necessarily some multiple of 10 by 10

00:11 We moved the point 3 times to the right

00:14 Therefore we'll add three zeros to the denominator

00:18 Place the digits in the numerator

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

Convert 0.708 into a fraction.

Step-by-step solution

To solve this problem, we will convert 0.708 into a fraction step-by-step:

Step 1: Identify the decimal and its place value. Since 0.708 has three decimal places, it is equivalent to having a denominator of 1000.
Step 2: Write the decimal as a fraction. Place the number 708 on the numerator and 1000 as the denominator, resulting in $\frac{708}{1000}$ .

Therefore, the solution to converting 0.708 to a fraction is $\frac{708}{1000}$ .

Final Answer

$\frac{708}{1000}$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Three decimal places means denominator is 1000
Technique: Write 0.708 as $\frac{708}{1000}$ using place value
Check: Divide 708 ÷ 1000 = 0.708 to verify ✓

Common Mistakes

Avoid these frequent errors

Using wrong denominator based on decimal places
Don't count decimal places incorrectly and use 100 or 10000 as denominator = wrong fraction! This happens when you miscount the digits after the decimal point. Always count carefully: 0.708 has exactly 3 decimal places, so the denominator must be 1000.

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

How do I know what denominator to use?

Count the decimal places! One place = 10, two places = 100, three places = 1000. Since 0.708 has three decimal places, use 1000 as your denominator.

Should I simplify the fraction after converting?

The question asks for the conversion, so $\frac{708}{1000}$ is the correct answer. You could simplify it to $\frac{177}{250}$ , but that's not required here.

What if the decimal has zeros at the end?

Still count all decimal places! For example, 0.750 has three decimal places, so it becomes $\frac{750}{1000}$ , even though the last digit is zero.

How can I check if my fraction is correct?

Divide the numerator by the denominator using long division or a calculator. If you get back to your original decimal, you're correct!

Why can't I use 100 as the denominator for 0.708?

Because 0.708 goes to the thousandths place, not the hundredths place. Using 100 would give you $\frac{708}{100}$ = 7.08, which is wrong!

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