Math / Numbers & Operations

QuestionWhat is the value of $\lfloor-1.1\rfloor$ ? $-2$ $-1$ 0 1

Studdy Solution

STEP 1

What is this asking? What is the greatest integer less than or equal to $-1.1$ ? Watch out! Don't mix up greatest and least, or greater than and less than!
Also, remember that negative numbers work in reverse!

STEP 2

1. Understand the floor function
2. Apply the floor function

STEP 3

The floor function, denoted by $\lfloor x \rfloor$ , takes any real number $x$ and rounds it down to the nearest integer.
It's like asking, "What's the biggest integer that's not bigger than $x$ ?".

STEP 4

For example, the floor of $3.14$ is $3$ .
Mathematically, $\lfloor 3.14 \rfloor = 3$ .
Even though $3.14$ is closer to $4$ , the floor function always rounds down.

STEP 5

Now, let's consider a negative number.
What's $\lfloor -0.5 \rfloor$ ?
It's $-1$ , not $0$ !
Remember, we're looking for the greatest integer less than or equal to $-0.5$ , and $-1$ is less than $-0.5$ , while $0$ is greater.

STEP 6

We want to find $\lfloor -1.1 \rfloor$ .
We're looking for the greatest integer less than or equal to $-1.1$ .

STEP 7

Since $-1$ is greater than $-1.1$ , it can't be the answer.
Think about the number line! $-1$ is to the right of $-1.1$ , so it's greater.

STEP 8

The next integer smaller than $-1$ is $-2$ .
Since $-2$ is less than $-1.1$ , and it's the largest integer that satisfies this condition, we've found our answer!

STEP 9

$\lfloor -1.1 \rfloor = -2$ .
So, the answer is $-2$ !

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QuestionWhat is the value of $\lfloor-1.1\rfloor$ ? $-2$ $-1$ 0 1

Studdy Solution

STEP 1

What is this asking? What is the greatest integer less than or equal to $-1.1$ ? Watch out! Don't mix up greatest and least, or greater than and less than!
Also, remember that negative numbers work in reverse!

STEP 2

1. Understand the floor function
2. Apply the floor function

STEP 3

The floor function, denoted by $\lfloor x \rfloor$ , takes any real number $x$ and rounds it down to the nearest integer.
It's like asking, "What's the biggest integer that's not bigger than $x$ ?".

STEP 4

For example, the floor of $3.14$ is $3$ .
Mathematically, $\lfloor 3.14 \rfloor = 3$ .
Even though $3.14$ is closer to $4$ , the floor function always rounds down.

STEP 5

Now, let's consider a negative number.
What's $\lfloor -0.5 \rfloor$ ?
It's $-1$ , not $0$ !
Remember, we're looking for the greatest integer less than or equal to $-0.5$ , and $-1$ is less than $-0.5$ , while $0$ is greater.

STEP 6

We want to find $\lfloor -1.1 \rfloor$ .
We're looking for the greatest integer less than or equal to $-1.1$ .

STEP 7

Since $-1$ is greater than $-1.1$ , it can't be the answer.
Think about the number line! $-1$ is to the right of $-1.1$ , so it's greater.

STEP 8

The next integer smaller than $-1$ is $-2$ .
Since $-2$ is less than $-1.1$ , and it's the largest integer that satisfies this condition, we've found our answer!

STEP 9

$\lfloor -1.1 \rfloor = -2$ .
So, the answer is $-2$ !

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QuestionWhat is the value of ⌊−1.1⌋\lfloor-1.1\rfloor⌊−1.1⌋ ? −2-2−2 −1-1−1 0 1

Studdy Solution

STEP 1

What is this asking? What is the greatest integer less than or equal to −1.1-1.1−1.1? Watch out! Don't mix up greatest and least, or greater than and less than!Also, remember that negative numbers work in reverse!

STEP 2

1. Understand the floor function2. Apply the floor function

STEP 3

The **floor function**, denoted by ⌊x⌋\lfloor x \rfloor⌊x⌋, takes any real number xxx and rounds it *down* to the nearest integer.It's like asking, "What's the biggest integer that's *not* bigger than xxx?".

STEP 4

For example, the floor of 3.143.143.14 is 333.Mathematically, ⌊3.14⌋=3\lfloor 3.14 \rfloor = 3⌊3.14⌋=3.Even though 3.143.143.14 is closer to 444, the floor function always rounds *down*.

STEP 5

Now, let's consider a negative number.What's ⌊−0.5⌋\lfloor -0.5 \rfloor⌊−0.5⌋?It's −1-1−1, not 000!Remember, we're looking for the greatest integer *less than or equal to* −0.5-0.5−0.5, and −1-1−1 is less than −0.5-0.5−0.5, while 000 is greater.

STEP 6

We want to find ⌊−1.1⌋\lfloor -1.1 \rfloor⌊−1.1⌋.We're looking for the greatest integer less than or equal to −1.1-1.1−1.1.

STEP 7

Since −1-1−1 is greater than −1.1-1.1−1.1, it can't be the answer.Think about the number line! −1-1−1 is to the *right* of −1.1-1.1−1.1, so it's greater.

STEP 8

The next integer smaller than −1-1−1 is −2-2−2.Since −2-2−2 is less than −1.1-1.1−1.1, and it's the largest integer that satisfies this condition, we've found our answer!

STEP 9

⌊−1.1⌋=−2\lfloor -1.1 \rfloor = -2⌊−1.1⌋=−2.So, the answer is −2-2−2!

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QuestionWhat is the value of $\lfloor-1.1\rfloor$ ? $-2$ $-1$ 0 1

What is this asking? What is the greatest integer less than or equal to $-1.1$ ? Watch out! Don't mix up greatest and least, or greater than and less than!
Also, remember that negative numbers work in reverse!

1. Understand the floor function
2. Apply the floor function

The floor function, denoted by $\lfloor x \rfloor$ , takes any real number $x$ and rounds it down to the nearest integer.
It's like asking, "What's the biggest integer that's not bigger than $x$ ?".

For example, the floor of $3.14$ is $3$ .
Mathematically, $\lfloor 3.14 \rfloor = 3$ .
Even though $3.14$ is closer to $4$ , the floor function always rounds down.

Now, let's consider a negative number.
What's $\lfloor -0.5 \rfloor$ ?
It's $-1$ , not $0$ !
Remember, we're looking for the greatest integer less than or equal to $-0.5$ , and $-1$ is less than $-0.5$ , while $0$ is greater.

We want to find $\lfloor -1.1 \rfloor$ .
We're looking for the greatest integer less than or equal to $-1.1$ .

Since $-1$ is greater than $-1.1$ , it can't be the answer.
Think about the number line! $-1$ is to the right of $-1.1$ , so it's greater.

The next integer smaller than $-1$ is $-2$ .
Since $-2$ is less than $-1.1$ , and it's the largest integer that satisfies this condition, we've found our answer!

$\lfloor -1.1 \rfloor = -2$ .
So, the answer is $-2$ !