Convert Decimal 1.711 to Fraction Form: Step-by-Step Solution

Q: Why is the denominator 1000 and not 100?

Count the decimal places! 1.711 has three digits after the decimal point (7, 1, 1). Three decimal places means thousandths, so the denominator is 1000.

Q: Do I need to simplify the fraction?

Yes, always check if you can simplify! For $ \frac{1711}{1000} $, find the GCD of 1711 and 1000. If they share no common factors other than 1, the fraction is already in lowest terms.

Q: What if the decimal has fewer places?

The rule stays the same! One decimal place → denominator 10Two decimal places → denominator 100Three decimal places → denominator 1000

Q: How do I remember which power of 10 to use?

Think of it this way: the number of zeros in the denominator equals the number of decimal places. Three decimal places = three zeros = 1000!

Q: Can I check my answer without a calculator?

Absolutely! Convert back by dividing: $ 1711 ÷ 1000 $. Since 1711 $ 1711 - 1000 = 711 $ gives you the decimal part: 1.711 ✓

Decimal to Fraction with Terminating Decimals

Convert into fraction form:

$1.711=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to fraction

00:03 First match between the digit position and the appropriate division

00:07 Add 1 to the fraction

00:10 Place the digits after the decimal point in the numerator

00:14 And the position of the last digit in the denominator

00:19 Convert from decimal to whole fraction

00:25 Multiply by the common denominator

00:31 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 into fraction form:

$1.711=$

Step-by-step solution

Let's pay attention to where the decimal point is located in the number.

Remember:

One number after the zero represents tens

Two numbers after the zero represent hundreds

Three numbers after the zero represent thousands

And so on

In this case, there are three numbers after the zero, so the number is divided by 1000

We'll write the fraction in the following way and obtain the following:

$\frac{1711}{1000}$

Final Answer

$\frac{1711}{1000}$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Count decimal places to find denominator power of 10
Technique: Three decimal places means denominator is 1000, so $1.711 = \frac{1711}{1000}$
Check: Verify by dividing: $\frac{1711}{1000} = 1.711$ ✓

Common Mistakes

Avoid these frequent errors

Misreading the decimal digits
Don't write $\frac{1710}{1000}$ or $\frac{1700}{1000}$ when the decimal is 1.711! This happens when you rush and misread the digits. Always carefully read each digit after the decimal point: 1.711 means 1711 thousandths.

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 is the denominator 1000 and not 100?

Count the decimal places! 1.711 has three digits after the decimal point (7, 1, 1). Three decimal places means thousandths, so the denominator is 1000.

Do I need to simplify the fraction?

Yes, always check if you can simplify! For $\frac{1711}{1000}$ , find the GCD of 1711 and 1000. If they share no common factors other than 1, the fraction is already in lowest terms.

What if the decimal has fewer places?

The rule stays the same!

One decimal place → denominator 10
Two decimal places → denominator 100
Three decimal places → denominator 1000

How do I remember which power of 10 to use?

Think of it this way: the number of zeros in the denominator equals the number of decimal places. Three decimal places = three zeros = 1000!

Can I check my answer without a calculator?

Absolutely! Convert back by dividing: $1711 ÷ 1000$ . Since 1711 < 1000×2, the answer starts with 1, and $1711 - 1000 = 711$ gives you the decimal part: 1.711 ✓

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