Convert the Decimal Fraction: Expressing 22/1000 in Decimal Form

Q: Why do I move the decimal point left instead of right?

When dividing by powers of 10, you're making the number smaller, so the decimal moves left. Think of it this way: $ \frac{22}{1000} $ means 22 parts out of 1000, which is much smaller than 22 whole units!

Q: How do I know how many places to move the decimal?

Count the zeros in the denominator! 1000 has 3 zeros, so move 3 places. 100 has 2 zeros, so move 2 places. The number of zeros = number of places to move left.

Q: What if I don't have enough digits to move the decimal?

Add zeros to the left! For 22, imagine it as 22.0, then add zeros: 022.0, 0022.0. Now you can move the decimal 3 places left to get 0.022.

Q: How can I double-check my answer is correct?

Multiply your decimal answer by the original denominator: $ 0.022 \times 1000 = 22 $. If you get the original numerator, you're right!

Q: Why is 0.22 wrong if 22/100 = 0.22?

Great observation! You're thinking of $ \frac{22}{100} = 0.22 $, but our problem is $ \frac{22}{1000} $. The extra zero in 1000 means one more decimal place, making it 0.022.

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

00:08 Now according to the denominator, move the decimal point to the left

00:12 There are 3 zeros in the denominator, so we move 3 times to the left

00:23 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

$\frac{22}{1000}=$

2

Step-by-step solution

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

Step 1: Assess the fraction, identifying the denominator as 1000.
Step 2: Recognize that with the denominator as a power of 10, we move the decimal point a corresponding number of places in the numerator.
Step 3: Execute the conversion to decimal form by moving the decimal point.

Now, let's work through each step:
Step 1: We're given the fraction $\frac{22}{1000}$ .
Step 2: Since the denominator is 1000, which is $10^3$ , we will move the decimal point in the numerator (22) three places to the left.
Step 3: Moving the decimal point three places to the left in 22, we get 0.022.

Therefore, the solution to the problem is $0.022$ .

3

Final Answer

0.022

Key Points to Remember

Essential concepts to master this topic

Rule: Powers of 10 denominators determine decimal point placement
Technique: 1000 = 10³, so move decimal 3 places left
Check: Count decimal places: 0.022 has 3 places = 1000 denominator ✓

Common Mistakes

Avoid these frequent errors

Not moving decimal point enough places
Don't move decimal only 2 places for 22/1000 = 0.22! This ignores that 1000 needs 3 decimal places, giving ten times the correct answer. Always count zeros in denominator: 1000 has 3 zeros, so move decimal 3 places left.

Practice Quiz

Test your knowledge with interactive questions

How much of the whole does the shaded area (blue) represent?

FAQ

Everything you need to know about this question

Why do I move the decimal point left instead of right?

+

When dividing by powers of 10, you're making the number smaller, so the decimal moves left. Think of it this way: $\frac{22}{1000}$ means 22 parts out of 1000, which is much smaller than 22 whole units!

How do I know how many places to move the decimal?

+

Count the zeros in the denominator! 1000 has 3 zeros, so move 3 places. 100 has 2 zeros, so move 2 places. The number of zeros = number of places to move left.

What if I don't have enough digits to move the decimal?

+

Add zeros to the left! For 22, imagine it as 22.0, then add zeros: 022.0, 0022.0. Now you can move the decimal 3 places left to get 0.022.

How can I double-check my answer is correct?

+

Multiply your decimal answer by the original denominator: $0.022 \times 1000 = 22$ . If you get the original numerator, you're right!

Why is 0.22 wrong if 22/100 = 0.22?

+

Great observation! You're thinking of $\frac{22}{100} = 0.22$ , but our problem is $\frac{22}{1000}$ . The extra zero in 1000 means one more decimal place, making it 0.022.

🌟 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

Convert the Decimal Fraction: Expressing 22/1000 in Decimal Form

Decimal Conversion with Powers of Ten

❤️ Continue Your Math Journey!