Convert Mixed Number to Decimal: Solving 10 105/1000

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

Look at the denominator! 1000 has 3 zeros, so your decimal needs exactly 3 places. For 10 (1 zero) use 1 place, for 100 (2 zeros) use 2 places.

Q: What if the numerator has fewer digits than decimal places needed?

Add leading zeros! For example, if you need 3 decimal places but only have 2 digits like 75, write it as 0.075, not 0.75.

Q: Can I simplify the fraction first before converting?

You can, but it's often easier to convert directly. $ \frac{105}{1000} $ could become $ \frac{21}{200} $, but dividing 105 ÷ 1000 is simpler than 21 ÷ 200.

Q: How do I check if my decimal conversion is correct?

Multiply your decimal by the original denominator: 0.105 × 1000 = 105. If you get the original numerator back, you're right!

Q: Why is 10.105 different from 10.15 or 10.5?

Each represents a different value! 10.105 means 10 and 105 thousandths, while 10.15 means 10 and 15 hundredths. The number of decimal places matters for the exact value.

Mixed Number Conversion with Thousandths

Convert $10\frac{105}{1000}$ into a decimal.

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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 Break down the number into whole number and remainder

00:17 When the denominator equals 100, place the numerator 3 digits after

00:31 Convert to decimal fraction

00:36 Use long addition for calculation

00:41 Calculate and substitute accordingly

01:02 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert $10\frac{105}{1000}$ into a decimal.

Step-by-step solution

To solve this problem, we will convert the given mixed number $10\frac{105}{1000}$ into a decimal.

Step 1: Convert the fractional part $\frac{105}{1000}$ to a decimal. We do this by dividing the numerator, $105$ , by the denominator, $1000$ .

$\frac{105}{1000} = 0.105$

Step 2: Add this decimal result to the whole number part. The whole number part is $10$ .

$10 + 0.105 = 10.105$

Therefore, the decimal representation of $10\frac{105}{1000}$ is $10.105$ .

Final Answer

10.105

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: Add whole number to decimal form of fraction
Technique: Divide 105 ÷ 1000 = 0.105, then add to 10
Check: Count decimal places: 105/1000 has 3 places = 0.105 ✓

Common Mistakes

Avoid these frequent errors

Adding decimal places incorrectly
Don't write 105/1000 as 0.15 or 0.0105! This happens when you don't count decimal places correctly. The denominator 1000 has 3 zeros, so 105/1000 must have exactly 3 decimal places: 0.105. Always match decimal places to the number of zeros.

Practice Quiz

Test your knowledge with interactive questions

Convert into fraction form:

$$ 0.38= $$

FAQ

Everything you need to know about this question

How do I know how many decimal places to use?

Look at the denominator! 1000 has 3 zeros, so your decimal needs exactly 3 places. For 10 (1 zero) use 1 place, for 100 (2 zeros) use 2 places.

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

Add leading zeros! For example, if you need 3 decimal places but only have 2 digits like 75, write it as 0.075, not 0.75.

Can I simplify the fraction first before converting?

You can, but it's often easier to convert directly. $\frac{105}{1000}$ could become $\frac{21}{200}$ , but dividing 105 ÷ 1000 is simpler than 21 ÷ 200.

How do I check if my decimal conversion is correct?

Multiply your decimal by the original denominator: 0.105 × 1000 = 105. If you get the original numerator back, you're right!

Why is 10.105 different from 10.15 or 10.5?

Each represents a different value! 10.105 means 10 and 105 thousandths, while 10.15 means 10 and 15 hundredths. The number of decimal places matters for the exact value.

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