Convert Fraction to Decimal: Solving 67/1000 Step by Step

Fraction to Decimal with Thousandths

Convert 671000 \frac{67}{1000} into a decimal.

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's convert this to a decimal fraction.
00:08 Count the number of zeros in the denominator.
00:12 With three zeros, move the decimal point 3 places left.
00:18 Place the numerator so there are three digits after the decimal.
00:23 Fill any missing spots with zero.
00:26 And that's how you find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Convert 671000 \frac{67}{1000} into a decimal.

2

Step-by-step solution

To convert the fraction 671000\frac{67}{1000} into a decimal, we recognize that the denominator 1000 implies that this fraction can be expressed in the thousandths place of a decimal.

  • Step 1: Identify that the fraction 671000\frac{67}{1000} needs to be expressed with three decimal places.
  • Step 2: Understand that each place value after the decimal corresponds to tenths, hundredths, and thousandths, respectively. Since we have 67 thousandths, the decimal will have three digits after the decimal point.
  • Step 3: Place 67 into the decimal system by placing it three places to the right of the decimal point:

We write it as 0.0670.067. Here, "0.0" represents there are no tenths or hundredths, and "67" fills the thousandths place.

Therefore, the decimal equivalent of 671000\frac{67}{1000} is 0.067\mathbf{0.067}.

3

Final Answer

0.067

Key Points to Remember

Essential concepts to master this topic
  • Place Value Rule: Denominator 1000 means three decimal places
  • Method: Place 67 in thousandths position: 0.067
  • Verification: Check that 0.067 × 1000 equals 67 ✓

Common Mistakes

Avoid these frequent errors
  • Misplacing decimal point based on denominator
    Don't just write 0.67 because you see two digits in 67 = wrong decimal place! This ignores that 1000 requires three decimal places. Always count the zeros in the denominator to determine decimal places.

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 where to place the decimal point?

+

Count the zeros in the denominator! Since 1000 has 3 zeros, you need 3 decimal places. So 671000 \frac{67}{1000} becomes 0.067.

Why isn't the answer 0.67?

+

Because 0.67 = 67/100, not 67/1000! The denominator 1000 means thousandths, so you need that extra zero: 0.067.

What if the numerator has more digits than decimal places needed?

+

That can't happen with proper fractions! If your numerator is bigger than the denominator, you have a mixed number or improper fraction to convert first.

How can I check if my decimal is correct?

+

Multiply your decimal by the original denominator. If 0.067 × 1000 = 67, you're right! This should equal your original numerator.

Do I always need zeros before the numerator digits?

+

Yes, when the numerator has fewer digits than decimal places needed! 671000 \frac{67}{1000} needs 3 places but 67 is only 2 digits, so add a leading zero: 0.067.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Decimal Fractions - Basic questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations