Identifying a Thousandth: Decimal Fraction Notation Exercise

Q: How do I remember which decimal represents a thousandth?

Think of the denominator 1000 - it has three zeros, so the decimal needs three places after the decimal point: 0.001!

Q: What's the difference between 0.01 and 0.001?

0.01 is one hundredth (1/100) while 0.001 is one thousandth (1/1000). The extra zero makes it ten times smaller!

Q: Why isn't 1000.0 the answer if we're talking about thousands?

That's one thousand, not one thousandth! A thousandth is the fraction $ \frac{1}{1000} $, which is much smaller than 1.

Q: How can I check if 0.001 really equals one thousandth?

Convert it back to a fraction: 0.001 = $ \frac{1}{1000} $. The three decimal places match the three zeros in 1000!

Decimal Place Values with Thousandths

Which answer shows a thousandth written as a decimal fraction?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which answer shows a thousandth written as a decimal fraction?

Step-by-step solution

To solve this problem, we will follow these steps:

Step 1: Recognize that a "thousandth" refers to the fraction $\frac{1}{1000}$ .
Step 2: Convert the fraction $\frac{1}{1000}$ to its decimal representation.
Step 3: Determine which of the given options matches this decimal representation.

Now, let's examine each step:
Step 1: A fraction representing a thousandth is $\frac{1}{1000}$ .
Step 2: When we convert $\frac{1}{1000}$ into a decimal, we see that it equals $0.001$ because it requires moving the decimal three places to the left, indicating three zeros before the digit 1.
Step 3: Among the choices provided, option 4 identifies a decimal representation of $0.001$ , which correctly reflects a single thousandth place.

Therefore, the solution to the problem is $0.001$ .

Final Answer

0.001

Key Points to Remember

Essential concepts to master this topic

Concept: A thousandth means one part out of 1000 equal parts
Technique: Convert $\frac{1}{1000}$ by moving decimal three places left: 0.001
Check: Count decimal places: 0.001 has three places, matching thousandths ✓

Common Mistakes

Avoid these frequent errors

Confusing thousandths with other place values
Don't mix up 0.1 (tenths), 0.01 (hundredths), and 0.001 (thousandths) = wrong place value! Each additional zero moves one decimal place further right. Always count the decimal places: thousandths need exactly three places after the decimal point.

Practice Quiz

Test your knowledge with interactive questions

Which figure represents 0.1?

FAQ

Everything you need to know about this question

How do I remember which decimal represents a thousandth?

Think of the denominator 1000 - it has three zeros, so the decimal needs three places after the decimal point: 0.001!

What's the difference between 0.01 and 0.001?

0.01 is one hundredth (1/100) while 0.001 is one thousandth (1/1000). The extra zero makes it ten times smaller!

Why isn't 1000.0 the answer if we're talking about thousands?

That's one thousand, not one thousandth! A thousandth is the fraction $\frac{1}{1000}$ , which is much smaller than 1.

How can I check if 0.001 really equals one thousandth?

Convert it back to a fraction: 0.001 = $\frac{1}{1000}$ . The three decimal places match the three zeros in 1000!

What comes after thousandths in decimal places?

Ten-thousandths (0.0001), then hundred-thousandths (0.00001). Each position gets ten times smaller as you move right.

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