Question
Compare 364,879; 463,000; and 436,765 using scientific notation. Which number has the least value?(1 point)
Responses
4.36765 ×105
4.36765 times 10 superscript 5 baseline
3.64879 ×105
3.64879 times 10 superscript 5 baseline
4.63 ×105
4.63 times 10 superscript 5 baseline
364,879
Use scientific notation to compare these numbers: 12,740,876,635; 1,345,763,334; and 12,920,370,000, which has the greatest value?(1 point)
Responses
1.345763334×109
1.345763334 times 10 superscript 9 baseline
12,920,370,000
12,920,370,000
1.292037×1010
1.292037 times 10 superscript 10 baseline
1.2740876635×1010
Compare 7.6 × 10−25
and 6.7 × 10−52
. Which statement is true?(1 point)
Responses
7.6 × 10−25 < 6.7 × 10−52
7.6 times 10 Superscript negative 25 Baseline is less than 6.7 times 10 Superscript negative 52 Baseline
7.6 × 10−25 = 6.7 × 10−52
7.6 times 10 Superscript negative 25 Baseline equals 6.7 times 10 Superscript negative 52 Baseline
7.6 × 10−25 > 6.7 × 10−52
7.6 times 10 Superscript negative 25 Baseline is greater than 6.7 times 10 Superscript negative 52 Baseline
7.6 × 10−25 ≤ 6.7 × 10−52
Which set of numbers is arranged in descending order?(1 point)
Responses
7.2 × 10−30
, 7 × 10−30
, 7.6 × 10−25
, 7.2 × 10−25
7.2 times 10 Superscript negative 30 Baseline , 7 times 10 Superscript negative 30 Baseline , 7.6 times 10 Superscript negative 25 Baseline , 7.2 times 10 Superscript negative 25 Baseline
7.6 × 10−25
, 7.2 × 10−25
, 7.2 × 10−30
, 7 × 10−30
7.6 times 10 Superscript negative 25 Baseline , 7.2 times 10 Superscript negative 25 Baseline , 7.2 times 10 Superscript negative 30 Baseline , 7 times 10 Superscript negative 30 Baseline
7.6 × 10−25
, 7.2 × 10−30
, 7.2 × 10−25
, 7 × 10−30
7.6 times 10 Superscript negative 25 Baseline , 7.2 times 10 Superscript negative 30 Baseline , 7.2 times 10 Superscript negative 25 Baseline , 7 times 10 Superscript negative 30 Baseline
7 × 10−30
, 7.2 × 10−25
, 7.2 × 10−30
, 7.6 × 10−25
In which set are the numbers arranged in ascending order?(1 point)
Responses
0.00125, 0.00225, 0.000325, 0.00325
0.00125, 0.00225, 0.000325, 0.00325
0.000325, 0.00225, 0.00125, 0.00325
0.000325, 0.00225, 0.00125, 0.00325
3.25 × 10−4
, 1.25 × 10−3
, 2.25 × 10−3
, 3.25 × 10−3
3.25 times 10 Superscript negative 4 Baseline , 1.25 times 10 Superscript negative 3 Baseline , 2.25 times 10 Superscript negative 3 Baseline , 3.25 times 10 Superscript negative 3 Baseline
3.25 × 10−3
, 2.25 × 10−3
, 3.25 × 10−4
, 1.25 × 10−3
Responses
4.36765 ×105
4.36765 times 10 superscript 5 baseline
3.64879 ×105
3.64879 times 10 superscript 5 baseline
4.63 ×105
4.63 times 10 superscript 5 baseline
364,879
Use scientific notation to compare these numbers: 12,740,876,635; 1,345,763,334; and 12,920,370,000, which has the greatest value?(1 point)
Responses
1.345763334×109
1.345763334 times 10 superscript 9 baseline
12,920,370,000
12,920,370,000
1.292037×1010
1.292037 times 10 superscript 10 baseline
1.2740876635×1010
Compare 7.6 × 10−25
and 6.7 × 10−52
. Which statement is true?(1 point)
Responses
7.6 × 10−25 < 6.7 × 10−52
7.6 times 10 Superscript negative 25 Baseline is less than 6.7 times 10 Superscript negative 52 Baseline
7.6 × 10−25 = 6.7 × 10−52
7.6 times 10 Superscript negative 25 Baseline equals 6.7 times 10 Superscript negative 52 Baseline
7.6 × 10−25 > 6.7 × 10−52
7.6 times 10 Superscript negative 25 Baseline is greater than 6.7 times 10 Superscript negative 52 Baseline
7.6 × 10−25 ≤ 6.7 × 10−52
Which set of numbers is arranged in descending order?(1 point)
Responses
7.2 × 10−30
, 7 × 10−30
, 7.6 × 10−25
, 7.2 × 10−25
7.2 times 10 Superscript negative 30 Baseline , 7 times 10 Superscript negative 30 Baseline , 7.6 times 10 Superscript negative 25 Baseline , 7.2 times 10 Superscript negative 25 Baseline
7.6 × 10−25
, 7.2 × 10−25
, 7.2 × 10−30
, 7 × 10−30
7.6 times 10 Superscript negative 25 Baseline , 7.2 times 10 Superscript negative 25 Baseline , 7.2 times 10 Superscript negative 30 Baseline , 7 times 10 Superscript negative 30 Baseline
7.6 × 10−25
, 7.2 × 10−30
, 7.2 × 10−25
, 7 × 10−30
7.6 times 10 Superscript negative 25 Baseline , 7.2 times 10 Superscript negative 30 Baseline , 7.2 times 10 Superscript negative 25 Baseline , 7 times 10 Superscript negative 30 Baseline
7 × 10−30
, 7.2 × 10−25
, 7.2 × 10−30
, 7.6 × 10−25
In which set are the numbers arranged in ascending order?(1 point)
Responses
0.00125, 0.00225, 0.000325, 0.00325
0.00125, 0.00225, 0.000325, 0.00325
0.000325, 0.00225, 0.00125, 0.00325
0.000325, 0.00225, 0.00125, 0.00325
3.25 × 10−4
, 1.25 × 10−3
, 2.25 × 10−3
, 3.25 × 10−3
3.25 times 10 Superscript negative 4 Baseline , 1.25 times 10 Superscript negative 3 Baseline , 2.25 times 10 Superscript negative 3 Baseline , 3.25 times 10 Superscript negative 3 Baseline
3.25 × 10−3
, 2.25 × 10−3
, 3.25 × 10−4
, 1.25 × 10−3
Answers
Answered by
GPT-4o mini
Let's address each of your questions one by one.
**1. Comparing 364,879; 463,000; and 436,765 in scientific notation:**
Convert each number to scientific notation:
- 364,879 = \(3.64879 \times 10^5\)
- 463,000 = \(4.63 \times 10^5\)
- 436,765 = \(4.36765 \times 10^5\)
Now, let's compare:
- \(3.64879 \times 10^5 < 4.36765 \times 10^5 < 4.63 \times 10^5\)
**The number with the least value is \(364,879\) (or \(3.64879 \times 10^5\)).**
---
**2. Comparing 12,740,876,635; 1,345,763,334; and 12,920,370,000 in scientific notation:**
Convert each number to scientific notation:
- 12,740,876,635 = \(1.2740876635 \times 10^{10}\)
- 1,345,763,334 = \(1.345763334 \times 10^9\)
- 12,920,370,000 = \(1.292037 \times 10^{10}\)
Now, let's compare:
- \(1.345763334 \times 10^9\) is smaller than both \(1.2740876635 \times 10^{10}\) and \(1.292037 \times 10^{10}\)
Comparing the numbers in the \(10^{10}\) range:
- \(1.2740876635 < 1.292037\)
**The number with the greatest value is \(12,920,370,000\) (or \(1.292037 \times 10^{10}\)).**
---
**3. Comparing \(7.6 \times 10^{-25}\) and \(6.7 \times 10^{-52}\):**
Since \(10^{-25}\) is greater than \(10^{-52}\), we can tell right away that:
- \(7.6 \times 10^{-25} > 6.7 \times 10^{-52}\)
**So the statement that is true is:** \(7.6 \times 10^{-25} > 6.7 \times 10^{-52}\).
---
**4. Arranging the set of numbers in descending order:**
Given:
- \(7.2 \times 10^{-30}\)
- \(7 \times 10^{-30}\)
- \(7.6 \times 10^{-25}\)
- \(7.2 \times 10^{-25}\)
The largest exponent is \(-25\) (in \(7.6 \times 10^{-25}\) and \(7.2 \times 10^{-25}\)), both are greater than those with exponent \(-30\). Hence, we need to sort as follows:
1. \(7.6 \times 10^{-25}\)
2. \(7.2 \times 10^{-25}\)
3. \(7.2 \times 10^{-30}\)
4. \(7 \times 10^{-30}\)
**The correct order in descending is:** \(7.6 \times 10^{-25}, 7.2 \times 10^{-25}, 7.2 \times 10^{-30}, 7 \times 10^{-30}\).
---
**5. Arranging the numbers in ascending order:**
Given:
- 0.00125
- 0.00225
- 0.000325
- 0.00325
If we convert them to scientific notation:
- 0.00125 = \(1.25 \times 10^{-3}\)
- 0.00225 = \(2.25 \times 10^{-3}\)
- 0.000325 = \(3.25 \times 10^{-4}\)
- 0.00325 = \(3.25 \times 10^{-3}\)
Arranging them from smallest to largest:
1. \(3.25 \times 10^{-4}\)
2. \(1.25 \times 10^{-3}\)
3. \(2.25 \times 10^{-3}\)
4. \(3.25 \times 10^{-3}\)
**The set arranged in ascending order is:** \(3.25 \times 10^{-4}, 1.25 \times 10^{-3}, 2.25 \times 10^{-3}, 3.25 \times 10^{-3}\).
Feel free to let me know if you have any further questions!
**1. Comparing 364,879; 463,000; and 436,765 in scientific notation:**
Convert each number to scientific notation:
- 364,879 = \(3.64879 \times 10^5\)
- 463,000 = \(4.63 \times 10^5\)
- 436,765 = \(4.36765 \times 10^5\)
Now, let's compare:
- \(3.64879 \times 10^5 < 4.36765 \times 10^5 < 4.63 \times 10^5\)
**The number with the least value is \(364,879\) (or \(3.64879 \times 10^5\)).**
---
**2. Comparing 12,740,876,635; 1,345,763,334; and 12,920,370,000 in scientific notation:**
Convert each number to scientific notation:
- 12,740,876,635 = \(1.2740876635 \times 10^{10}\)
- 1,345,763,334 = \(1.345763334 \times 10^9\)
- 12,920,370,000 = \(1.292037 \times 10^{10}\)
Now, let's compare:
- \(1.345763334 \times 10^9\) is smaller than both \(1.2740876635 \times 10^{10}\) and \(1.292037 \times 10^{10}\)
Comparing the numbers in the \(10^{10}\) range:
- \(1.2740876635 < 1.292037\)
**The number with the greatest value is \(12,920,370,000\) (or \(1.292037 \times 10^{10}\)).**
---
**3. Comparing \(7.6 \times 10^{-25}\) and \(6.7 \times 10^{-52}\):**
Since \(10^{-25}\) is greater than \(10^{-52}\), we can tell right away that:
- \(7.6 \times 10^{-25} > 6.7 \times 10^{-52}\)
**So the statement that is true is:** \(7.6 \times 10^{-25} > 6.7 \times 10^{-52}\).
---
**4. Arranging the set of numbers in descending order:**
Given:
- \(7.2 \times 10^{-30}\)
- \(7 \times 10^{-30}\)
- \(7.6 \times 10^{-25}\)
- \(7.2 \times 10^{-25}\)
The largest exponent is \(-25\) (in \(7.6 \times 10^{-25}\) and \(7.2 \times 10^{-25}\)), both are greater than those with exponent \(-30\). Hence, we need to sort as follows:
1. \(7.6 \times 10^{-25}\)
2. \(7.2 \times 10^{-25}\)
3. \(7.2 \times 10^{-30}\)
4. \(7 \times 10^{-30}\)
**The correct order in descending is:** \(7.6 \times 10^{-25}, 7.2 \times 10^{-25}, 7.2 \times 10^{-30}, 7 \times 10^{-30}\).
---
**5. Arranging the numbers in ascending order:**
Given:
- 0.00125
- 0.00225
- 0.000325
- 0.00325
If we convert them to scientific notation:
- 0.00125 = \(1.25 \times 10^{-3}\)
- 0.00225 = \(2.25 \times 10^{-3}\)
- 0.000325 = \(3.25 \times 10^{-4}\)
- 0.00325 = \(3.25 \times 10^{-3}\)
Arranging them from smallest to largest:
1. \(3.25 \times 10^{-4}\)
2. \(1.25 \times 10^{-3}\)
3. \(2.25 \times 10^{-3}\)
4. \(3.25 \times 10^{-3}\)
**The set arranged in ascending order is:** \(3.25 \times 10^{-4}, 1.25 \times 10^{-3}, 2.25 \times 10^{-3}, 3.25 \times 10^{-3}\).
Feel free to let me know if you have any further questions!
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