Convert Fraction to Decimal: Solving 105/1000 Step by Step

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

When you divide by a power of 10 like 1000, you're making the number smaller. Moving left makes it smaller, while moving right makes it bigger. Think: $ \frac{105}{1000} $ must be less than 105!

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 decimal places to move.

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

Add leading zeros as needed! For $ \frac{5}{1000} $, start with 5.0, then add zeros: 005.0 → 0.005. You can always add zeros to the left of a number.

Q: Can I just divide 105 by 1000 on a calculator?

Yes, but understanding the decimal point movement helps you work without a calculator and catch mistakes! Plus, it's faster for powers of 10 once you know the pattern.

Q: What's the difference between 0.105 and 0.1050?

They're mathematically equal! Extra zeros at the end of decimals don't change the value. However, 0.105 is the simplest form since we don't need the trailing zero.

Fraction to Decimal with Power of Ten Denominators

Convert to decimal fraction $\frac{105}{1000}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's convert this to a decimal fraction.

00:09 Count the zeros in the denominator. This tells us how many times to move the decimal point to the left.

00:16 Here, we have three zeros, so move the decimal point three places to the left.

00:22 Now, place the numerator after the decimal point.

00:26 And there you go! That's the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert to decimal fraction $\frac{105}{1000}$

Step-by-step solution

To convert the fraction $\frac{105}{1000}$ to a decimal, note that the denominator, 1000, is $10^3$ , which means we need to move the decimal point three places to the left in the numerator.

Let's break it down:

Start with the numerator, 105, which can be viewed as 105.0 for clarity.
Since the denominator is 1000, move the decimal three places to the left: $105.0 \rightarrow 10.5 \rightarrow 1.05 \rightarrow 0.105$

This places the decimal correctly according to the denominator's power of ten.

Therefore, the decimal representation of $\frac{105}{1000}$ is 0.105.

Final Answer

0.105

Key Points to Remember

Essential concepts to master this topic

Rule: When denominator is a power of 10, move decimal left
Technique: For 1000 = $10^3$ , move decimal 3 places: 105.0 → 0.105
Check: Multiply back: 0.105 × 1000 = 105 ✓

Common Mistakes

Avoid these frequent errors

Moving decimal point in wrong direction
Don't move the decimal point right when dividing by powers of 10 = numbers greater than 1! This makes your answer 100 or 1000 times too big. Always move decimal left when dividing by 10, 100, 1000, etc.

Practice Quiz

Test your knowledge with interactive questions

Write the following fraction as a decimal:

$\frac{1}{100}=$

FAQ

Everything you need to know about this question

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

When you divide by a power of 10 like 1000, you're making the number smaller. Moving left makes it smaller, while moving right makes it bigger. Think: $\frac{105}{1000}$ must be less than 105!

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 decimal places to move.

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

Add leading zeros as needed! For $\frac{5}{1000}$ , start with 5.0, then add zeros: 005.0 → 0.005. You can always add zeros to the left of a number.

Can I just divide 105 by 1000 on a calculator?

Yes, but understanding the decimal point movement helps you work without a calculator and catch mistakes! Plus, it's faster for powers of 10 once you know the pattern.

How do I check if my decimal answer is correct?

Multiply your decimal by the original denominator. For 0.105 × 1000 = 105, which matches our numerator! If you get the original numerator, your answer is right.

What's the difference between 0.105 and 0.1050?

They're mathematically equal! Extra zeros at the end of decimals don't change the value. However, 0.105 is the simplest form since we don't need the trailing zero.

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