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

Determine the numerical value of the shaded area:

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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