Find the Opposite Number: Converting 2.1 to Its Negative Value

Q: What's the difference between reciprocal and opposite?

The reciprocal is what you multiply by to get 1, while the opposite is what you add to get 0. For 2.1: reciprocal is $ \frac{10}{21} $, opposite is -2.1.

Q: Can I just flip 2.1 directly without converting to a fraction?

No! You can't flip a decimal directly. You must first convert 2.1 to the fraction $ \frac{21}{10} $, then flip it to get $ \frac{10}{21} $.

Q: How do I check if my reciprocal is correct?

Multiply the original number by your answer. If you get exactly 1, your reciprocal is correct! For example: $ 2.1 \times \frac{10}{21} = \frac{21}{10} \times \frac{10}{21} = 1 $

Q: Why is the question title about 'opposite number' but asking for reciprocal?

This appears to be a mislabeling in the question. The actual problem asks for reciprocal form, and the correct answer $ \frac{10}{21} $ confirms this. Always read the question content carefully!

Reciprocal Calculations with Decimal Numbers

Convert $2.1$ into its reciprocal form:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the reciprocal of a number. It's like flipping the fraction!

00:08 First, break down the number into a whole number and a remainder.

00:13 Now, change this decimal into a fraction. Isn't that neat?

00:19 Next, turn the whole number into a proper fraction too.

00:26 Add these fractions together using a common denominator. Great job so far!

00:41 Let's use the formula to get the reciprocal of this number.

00:46 Remember, any number times its reciprocal equals 1.

00:50 Just swap the numerator and denominator to find the reciprocal.

00:55 And that's how we solve it! You've done excellent work!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert $2.1$ into its reciprocal form:

Step-by-step solution

To solve the problem, let's follow these steps:

Step 1: Convert $2.1$ to a fraction.
Step 2: Find the reciprocal of this fraction.
Step 3: Simplify the reciprocal.

Now, let's execute each step:

Step 1: Convert $2.1$ to a fraction. Since $2.1$ is a decimal, we express it as a fraction: $2.1 = \frac{21}{10}$ .

Step 2: Find the reciprocal. The reciprocal of $\frac{21}{10}$ is $\frac{10}{21}$ .

Step 3: Simplify. The fraction $\frac{10}{21}$ is already in its simplest form.

Thus, the reciprocal of $2.1$ is $\frac{10}{21}$ , which corresponds to choice 4.

Therefore, the opposite number of $2.1$ , interpreted as its reciprocal, is $\frac{10}{21}$ .

Final Answer

$\frac{10}{21}$

Key Points to Remember

Essential concepts to master this topic

Definition: Reciprocal means flip the fraction to get multiplicative inverse
Technique: Convert 2.1 to $\frac{21}{10}$ , then flip to $\frac{10}{21}$
Check: Multiply original by reciprocal: $2.1 \times \frac{10}{21} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Confusing reciprocal with opposite (negative)
Don't think reciprocal means negative like -2.1 = wrong concept! The reciprocal is about division, not subtraction. Always remember: reciprocal means flip the fraction, not change the sign.

Practice Quiz

Test your knowledge with interactive questions

Convert $\frac{7}{2}$ into its reciprocal form:

FAQ

Everything you need to know about this question

What's the difference between reciprocal and opposite?

The reciprocal is what you multiply by to get 1, while the opposite is what you add to get 0. For 2.1: reciprocal is $\frac{10}{21}$ , opposite is -2.1.

How do I convert a decimal to a fraction for finding reciprocals?

Move the decimal point to make a whole number, then put it over the appropriate power of 10. For example: 2.1 = 21/10 (moved decimal 1 place, so divide by 10).

Can I just flip 2.1 directly without converting to a fraction?

No! You can't flip a decimal directly. You must first convert 2.1 to the fraction $\frac{21}{10}$ , then flip it to get $\frac{10}{21}$ .

How do I check if my reciprocal is correct?

Multiply the original number by your answer. If you get exactly 1, your reciprocal is correct! For example: $2.1 \times \frac{10}{21} = \frac{21}{10} \times \frac{10}{21} = 1$

Why is the question title about 'opposite number' but asking for reciprocal?

This appears to be a mislabeling in the question. The actual problem asks for reciprocal form, and the correct answer $\frac{10}{21}$ confirms this. Always read the question content carefully!

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