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

Write the following fraction as a decimal:

$\frac{5}{100}=$

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.

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

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