Find the Inverse Number: Converting 0.7 to Its Reciprocal

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

Great question! The inverse number (or additive inverse) is the opposite: $ 0.7 $ becomes $ -0.7 $. The reciprocal (multiplicative inverse) is $ \frac{1}{0.7} $. They're completely different!

Q: Why is the answer negative when the original is positive?

The additive inverse must have the opposite sign so that when you add them together, you get zero. Since $ 0.7 $ is positive, its inverse must be negative: $ 0.7 + (-0.7) = 0 $.

Q: How do I remember which type of inverse to find?

Look for key words! 'Inverse number' or 'opposite' means additive inverse (change the sign). 'Reciprocal' means multiplicative inverse (flip the fraction). When in doubt, check if adding gives zero!

Q: What if the number was already negative?

If you start with a negative number like $ -3.2 $, its additive inverse would be positive: $ 3.2 $. The rule is always the same: change the sign!

Additive Inverse with Decimal Numbers

What is the inverse number of $0.7$

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Understand the problem

What is the inverse number of $0.7$

Step-by-step solution

To determine the opposite number of $0.7$ , we will simply change its sign, following these steps:

Step 1: Identify the given number, which is $0.7$ .
Step 2: Change the sign of $0.7$ to find its opposite. Since $0.7$ is positive, its opposite will be negative.

By changing the sign of $0.7$ , we get $-0.7$ . Therefore, the opposite number of $0.7$ is $-0.7$ .

In conclusion, the solution to the problem is $-0.7$ .

Final Answer

$-0.7$

Key Points to Remember

Essential concepts to master this topic

Definition: The inverse number is the additive inverse (opposite)
Technique: Change the sign: $0.7$ becomes $-0.7$
Check: Add original and inverse: $0.7 + (-0.7) = 0$ ✓

Common Mistakes

Avoid these frequent errors

Confusing additive inverse with multiplicative inverse
Don't think the inverse of $0.7$ is $\frac{1}{0.7}$ = wrong type of inverse! The question asks for the inverse number, which means additive inverse (opposite), not reciprocal. Always change the sign to find the additive inverse.

Practice Quiz

Test your knowledge with interactive questions

a is negative number.

b is negative number.

What is the sum of a+b?

FAQ

Everything you need to know about this question

What's the difference between inverse and reciprocal?

Great question! The inverse number (or additive inverse) is the opposite: $0.7$ becomes $-0.7$ . The reciprocal (multiplicative inverse) is $\frac{1}{0.7}$ . They're completely different!

Why is the answer negative when the original is positive?

The additive inverse must have the opposite sign so that when you add them together, you get zero. Since $0.7$ is positive, its inverse must be negative: $0.7 + (-0.7) = 0$ .

Does every number have an inverse?

Yes! Every real number has an additive inverse. For any number a, its additive inverse is -a. Even zero has an inverse: the inverse of $0$ is $0$ itself.

How do I remember which type of inverse to find?

Look for key words! 'Inverse number' or 'opposite' means additive inverse (change the sign). 'Reciprocal' means multiplicative inverse (flip the fraction). When in doubt, check if adding gives zero!

What if the number was already negative?

If you start with a negative number like $-3.2$ , its additive inverse would be positive: $3.2$ . The rule is always the same: change the sign!

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