Convert Decimal to Words: Writing 0.110 in Standard Form

Q: Why does 0.110 need 1000 in the denominator instead of 100?

Because 0.110 has exactly 3 decimal places! Each decimal place represents a power of 10: tenths (10¹), hundredths (10²), and thousandths (10³). Since the last digit is in the thousandths place, we use 1000.

Q: What's the difference between 0.11 and 0.110?

Mathematically they're equal, but 0.110 shows more precision. When converting to words: 0.11 = "11 divided by 100" while 0.110 = "110 divided by 1000".

Q: Do I always include trailing zeros when converting?

Yes, when they're given in the problem! The trailing zero tells you the exact number of decimal places to count. This determines your denominator.

Decimal Conversion with Three-Digit Numerators

Rewrite the following decimal in words:

0.110

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Rewrite the following decimal in words:

0.110

Step-by-step solution

To solve this problem, we will follow these steps:

Step 1: Convert the decimal $0.110$ into a fraction.
Step 2: Express the fraction in words.

Let us work through each step:

Step 1: Convert the decimal to a fraction.
A decimal number is expressed as a fraction with the denominator as a power of 10, where the power corresponds to the number of decimal places. The decimal $0.110$ has three decimal places. Thus, it can be written as:

$0.110 = \frac{110}{1000}$ .

Step 2: Express the fraction in words.
The fraction $\frac{110}{1000}$ is read as "110 divided by 1000" in words. Therefore, the decimal $0.110$ in words is "110 divided by 1000".

The solution to the problem is $\text{"110 divided by 1000"}$ .

Final Answer

110 divided by 1000

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Count decimal places to determine denominator power
Technique: 0.110 has 3 places, so write as $\frac{110}{1000}$
Check: Divide 110 ÷ 1000 = 0.110 matches original ✓

Common Mistakes

Avoid these frequent errors

Ignoring trailing zeros in decimal places
Don't count 0.110 as having 2 decimal places because of the trailing zero = wrong denominator! This gives $\frac{11}{100} = 0.11$ , not 0.110. Always count every digit position after the decimal point, including trailing zeros.

Practice Quiz

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Determine the numerical value of the shaded area:

FAQ

Everything you need to know about this question

Why does 0.110 need 1000 in the denominator instead of 100?

Because 0.110 has exactly 3 decimal places! Each decimal place represents a power of 10: tenths (10¹), hundredths (10²), and thousandths (10³). Since the last digit is in the thousandths place, we use 1000.

What's the difference between 0.11 and 0.110?

Mathematically they're equal, but 0.110 shows more precision. When converting to words: 0.11 = "11 divided by 100" while 0.110 = "110 divided by 1000".

Do I always include trailing zeros when converting?

Yes, when they're given in the problem! The trailing zero tells you the exact number of decimal places to count. This determines your denominator.

How do I know if I can simplify the fraction?

Check if the numerator and denominator share common factors. For $\frac{110}{1000}$ , both divide by 10 to get $\frac{11}{100}$ , but the problem asks for the direct conversion.

What if the decimal has more than 3 places?

Same rule applies! Count every decimal place to find your denominator. 4 places = 10,000, 5 places = 100,000, and so on.

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