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

00:00 Find the reciprocal number

00:04 Break down the number into whole number and remainder

00:09 Convert from decimal to fraction

00:15 Convert from whole number to proper fraction

00:22 Add the fractions under a common denominator

00:37 Use the formula to find the reciprocal number

00:42 Any number multiplied by its reciprocal always equals 1

00:46 Switch between numerator and denominator to get the reciprocal number

00:51 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 $2.1$ 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

Solve the following exercise:

$(+6)\cdot(+9)=$

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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