Convert the Fraction 77/1000: Decimal Notation Practice

Fraction to Decimal with Powers of Ten

771000= \frac{77}{1000}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Convert to decimal fraction
00:03 Write the numerator as a number
00:09 Now according to the denominator, move the decimal point to the left
00:16 There are 3 zeros in the denominator, so we move 3 times to the left
00:27 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

771000= \frac{77}{1000}=

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Step-by-step solution

To solve this problem, we'll follow these steps:

  • Understand that 771000\frac{77}{1000} is a fraction where the denominator is a power of 10.
  • Recognize that the decimal equivalent can be found directly by placing the decimal point three places to the left of the numerator (since the denominator is 1000).
  • Write down the result.

Now, let's work through each step:

771000 \frac{77}{1000} means dividing 77 by 1000.

Step 1: Recognize that the denominator 1000 allows us to place the decimal point 3 positions to the left of the numerator.

Step 2: Start with 77, which can be viewed as 077 to ensure we can correctly place the decimal point.

Step 3: Move the decimal point three places left to get 0.0770.077.

Therefore, the solution to the problem is 0.077 0.077 .

3

Final Answer

0.077

Key Points to Remember

Essential concepts to master this topic
  • Rule: When denominator is 1000, move decimal point 3 places left
  • Technique: Convert 77 to 0.077 by placing decimal before the digits
  • Check: Count zeros in 1000 matches decimal places moved ✓

Common Mistakes

Avoid these frequent errors
  • Placing decimal point incorrectly
    Don't just divide 77 ÷ 1000 = 0.77! This ignores that 1000 has three zeros, not two. The decimal point must move exactly 3 places left from 77, giving 0.077. Always count the zeros in the denominator to know how many places to move.

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 does the decimal point move 3 places for 1000?

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The number of zeros in the denominator tells you how many places to move the decimal! 1000 has 3 zeros, so move 3 places left. For 100 (2 zeros), move 2 places.

What if my numerator doesn't have enough digits?

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Add leading zeros as needed! For 71000 \frac{7}{1000} , think of 7 as 007, then move 3 places left to get 0.007.

How can I check if 0.077 is correct?

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Multiply back: 0.077 × 1000 = 77. If you get your original numerator, you're right! This is the fastest way to verify.

Is there a difference between 0.077 and 0.77?

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Yes! 0.077 = 77 thousandths while 0.77 = 77 hundredths. The extra zero matters - it makes the number 10 times smaller.

What if I see 77/10 or 77/100 instead?

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Same method! For 77/10, move 1 place left → 7.7. For 77/100, move 2 places left → 0.77. Just count the zeros!

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