Question
Decide whether each statement is true. Choose Yes or No from the drop-down box.
3×10×10×10=3×103
Choose
400,000=4×106
Choose
7×105=7×100,000
Choose
5 × 1,000=5,000
Choose
3×10×10×10=3×103
Choose
400,000=4×106
Choose
7×105=7×100,000
Choose
5 × 1,000=5,000
Choose
Answers
Answer
Yari says that the product 230×104
has four zeroes. Is she correct? In the box below, explain your answer including how patterns for multiplying by powers of 10 help determine the final answer. Show your work to support your conclusion.
has four zeroes. Is she correct? In the box below, explain your answer including how patterns for multiplying by powers of 10 help determine the final answer. Show your work to support your conclusion.
Answer
The following question has two parts. First, answer part A. Then, answer part B.
Part A
Which of the following is the word form of 2,909?
(1 point)
Responses
two thousand ninety-nine
two thousand ninety-nine
two thousand ninety
two thousand ninety
two thousand nine hundred ninety
two thousand nine hundred ninety
two thousand nine hundred nine
Part A
Which of the following is the word form of 2,909?
(1 point)
Responses
two thousand ninety-nine
two thousand ninety-nine
two thousand ninety
two thousand ninety
two thousand nine hundred ninety
two thousand nine hundred ninety
two thousand nine hundred nine
Answer
Drag the values into the box to complete the expanded notation for 2,909. Numbers may be used once, more than once, or not at all.
(1 point)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
(2×
Response area ) + (9×
Response area ) + (9×
Response area)
(1 point)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
(2×
Response area ) + (9×
Response area ) + (9×
Response area)
Answer
What is the relationship between the value of the digit 3 in 4,231 and in the value of the digit 3 in the number 3,421?
(1 point)
Responses
In 4,231, the value of the digit 3 is 110
the value of the digit 3 in 3,421.
In 4,231, the value of the digit 3 is 1 10 the value of the digit 3 in 3,421.
In 4,231, the value of the digit 3 is 10 times the value of the digit 3 in 3,421.
In 4,231, the value of the digit 3 is 10 times the value of the digit 3 in 3,421.
In 4,231, the value of the digit 3 is 1100
the value of the digit 3 in 3,421.
In 4,231, the value of the digit 3 is 1 100 the value of the digit 3 in 3,421.
In 4,231, the value of the digit 3 is 100 times the value of the digit 3 in 3,421.
(1 point)
Responses
In 4,231, the value of the digit 3 is 110
the value of the digit 3 in 3,421.
In 4,231, the value of the digit 3 is 1 10 the value of the digit 3 in 3,421.
In 4,231, the value of the digit 3 is 10 times the value of the digit 3 in 3,421.
In 4,231, the value of the digit 3 is 10 times the value of the digit 3 in 3,421.
In 4,231, the value of the digit 3 is 1100
the value of the digit 3 in 3,421.
In 4,231, the value of the digit 3 is 1 100 the value of the digit 3 in 3,421.
In 4,231, the value of the digit 3 is 100 times the value of the digit 3 in 3,421.
Answer
Select a number to make the following statement true.
(1 point)
0.07 is 10 times as great as
Choose
.
(1 point)
0.07 is 10 times as great as
Choose
.
Answered by
GPT-4o mini
Let's evaluate each statement:
1. **3×10×10×10=3×10^3**
Yes, because 10×10×10 is 10 raised to the power of 3 (10^3).
**Answer: Yes**
2. **400,000=4×10^6**
No, because 4×10^6 is equal to 4,000,000, not 400,000.
**Answer: No**
3. **7×10^5=7×100,000**
Yes, because 10^5 is equal to 100,000.
**Answer: Yes**
4. **5 × 1,000=5,000**
Yes, because 5 multiplied by 1,000 equals 5,000.
**Answer: Yes**
So the answers are:
1. Yes
2. No
3. Yes
4. Yes
1. **3×10×10×10=3×10^3**
Yes, because 10×10×10 is 10 raised to the power of 3 (10^3).
**Answer: Yes**
2. **400,000=4×10^6**
No, because 4×10^6 is equal to 4,000,000, not 400,000.
**Answer: No**
3. **7×10^5=7×100,000**
Yes, because 10^5 is equal to 100,000.
**Answer: Yes**
4. **5 × 1,000=5,000**
Yes, because 5 multiplied by 1,000 equals 5,000.
**Answer: Yes**
So the answers are:
1. Yes
2. No
3. Yes
4. Yes
Answered by
GPT-4o mini
To evaluate Yari's claim that the product \( 230 \times 10^4 \) has four zeroes, let's break down the calculation and use the properties of multiplying by powers of 10.
### Step 1: Understanding Powers of 10
When multiplying by a power of 10, the number of zeroes added to the number depends on the exponent of 10. Specifically:
- \( 10^1 \) has 1 zero (10)
- \( 10^2 \) has 2 zeros (100)
- \( 10^3 \) has 3 zeros (1,000)
- \( 10^4 \) has 4 zeros (10,000)
### Step 2: Calculating the Product
When we multiply \( 230 \) by \( 10^4 \):
\[
230 \times 10^4 = 230 \times 10,000
\]
### Step 3: Applying the Multiplication
We can perform the multiplication explicitly:
1. \( 230 \) can be thought of as \( 230 \) and then we multiply by \( 10,000 \):
\[
230 \times 10,000 = 230,000
\]
### Step 4: Counting Zeroes
Now, let's count the zeroes in \( 230,000 \):
- The number \( 230,000 \) has **three** zeros.
### Conclusion
Since \( 230 \times 10^4 = 230,000 \), and there are only **three** zeros in the result, Yari is incorrect in stating that the product has four zeroes.
### Summary
Multiplying by \( 10^4 \) means you are effectively shifting the decimal point 4 places to the right, but you also have to consider the original number before you apply the multiplication. The key here is recognizing that \( 230 \) contributes to the significant digits and does not add additional zeros. Thus, the final conclusion is:
**Yari is incorrect; the product \( 230 \times 10^4 \) has three zeros, not four.**
### Step 1: Understanding Powers of 10
When multiplying by a power of 10, the number of zeroes added to the number depends on the exponent of 10. Specifically:
- \( 10^1 \) has 1 zero (10)
- \( 10^2 \) has 2 zeros (100)
- \( 10^3 \) has 3 zeros (1,000)
- \( 10^4 \) has 4 zeros (10,000)
### Step 2: Calculating the Product
When we multiply \( 230 \) by \( 10^4 \):
\[
230 \times 10^4 = 230 \times 10,000
\]
### Step 3: Applying the Multiplication
We can perform the multiplication explicitly:
1. \( 230 \) can be thought of as \( 230 \) and then we multiply by \( 10,000 \):
\[
230 \times 10,000 = 230,000
\]
### Step 4: Counting Zeroes
Now, let's count the zeroes in \( 230,000 \):
- The number \( 230,000 \) has **three** zeros.
### Conclusion
Since \( 230 \times 10^4 = 230,000 \), and there are only **three** zeros in the result, Yari is incorrect in stating that the product has four zeroes.
### Summary
Multiplying by \( 10^4 \) means you are effectively shifting the decimal point 4 places to the right, but you also have to consider the original number before you apply the multiplication. The key here is recognizing that \( 230 \) contributes to the significant digits and does not add additional zeros. Thus, the final conclusion is:
**Yari is incorrect; the product \( 230 \times 10^4 \) has three zeros, not four.**
Answered by
GPT-4o mini
The word form of the number 2,909 is **two thousand nine hundred nine**.
### Part A Answer:
**two thousand nine hundred nine**
### Part A Answer:
**two thousand nine hundred nine**
Answered by
GPT-4o mini
To express the number 2,909 in expanded notation, we break it down based on its place values:
- The digit **2** is in the thousands place, so it represents **2,000**.
- The digit **9** is in the hundreds place, so it represents **900**.
- The second digit **0** is in the tens place, which represents **0** (and does not need to be included in the notation).
- The last digit **9** is in the ones place, representing **9**.
So, the expanded notation for 2,909 can be expressed as:
\[
(2 \times 1,000) + (9 \times 100) + (0 \times 10) + (9 \times 1)
\]
However, typically we do not include the zero in expanded notation since it adds no value.
Thus, the final expanded notation would be:
\[
(2 \times 1,000) + (9 \times 100) + (9 \times 1)
\]
### Fill in the Responses:
- For the first response area: **1,000**
- For the second response area: **100**
- For the third response area: **1**
So the complete expanded notation for 2,909 is:
\[
(2 \times 1,000) + (9 \times 100) + (9 \times 1)
\]
- The digit **2** is in the thousands place, so it represents **2,000**.
- The digit **9** is in the hundreds place, so it represents **900**.
- The second digit **0** is in the tens place, which represents **0** (and does not need to be included in the notation).
- The last digit **9** is in the ones place, representing **9**.
So, the expanded notation for 2,909 can be expressed as:
\[
(2 \times 1,000) + (9 \times 100) + (0 \times 10) + (9 \times 1)
\]
However, typically we do not include the zero in expanded notation since it adds no value.
Thus, the final expanded notation would be:
\[
(2 \times 1,000) + (9 \times 100) + (9 \times 1)
\]
### Fill in the Responses:
- For the first response area: **1,000**
- For the second response area: **100**
- For the third response area: **1**
So the complete expanded notation for 2,909 is:
\[
(2 \times 1,000) + (9 \times 100) + (9 \times 1)
\]
Answered by
GPT-4o mini
To analyze the relationship between the value of the digit 3 in the two numbers, 4,231 and 3,421, we need to determine the place value of the digit 3 in each number.
1. **In the number 4,231:**
- The digit **3** is in the tens place, so its value is **30** (which is \(3 \times 10\)).
2. **In the number 3,421:**
- The digit **3** is in the thousands place, so its value is **3,000** (which is \(3 \times 1,000\)).
### Comparing the Values:
- Value of 3 in 4,231: **30**
- Value of 3 in 3,421: **3,000**
Now, let's find the relationship between them:
- **30** is **1/100** of **3,000**, meaning:
\[
30 = \frac{3,000}{100}
\]
Thus,
**The value of the digit 3 in 4,231 is 1/100 the value of the digit 3 in 3,421.**
### Conclusion:
Looking at the given response options, the correct choice would be:
**In 4,231, the value of the digit 3 is 100 times less than the value of the digit 3 in 3,421.** (which can be interpreted as \( \frac{1}{100} \times \) the value).
However, there might not be an exact option stating that, so based on what you provided, the closest response that correctly interprets the relationship is:
**In 4,231, the value of the digit 3 is 100 times less than the value of the digit 3 in 3,421.**
1. **In the number 4,231:**
- The digit **3** is in the tens place, so its value is **30** (which is \(3 \times 10\)).
2. **In the number 3,421:**
- The digit **3** is in the thousands place, so its value is **3,000** (which is \(3 \times 1,000\)).
### Comparing the Values:
- Value of 3 in 4,231: **30**
- Value of 3 in 3,421: **3,000**
Now, let's find the relationship between them:
- **30** is **1/100** of **3,000**, meaning:
\[
30 = \frac{3,000}{100}
\]
Thus,
**The value of the digit 3 in 4,231 is 1/100 the value of the digit 3 in 3,421.**
### Conclusion:
Looking at the given response options, the correct choice would be:
**In 4,231, the value of the digit 3 is 100 times less than the value of the digit 3 in 3,421.** (which can be interpreted as \( \frac{1}{100} \times \) the value).
However, there might not be an exact option stating that, so based on what you provided, the closest response that correctly interprets the relationship is:
**In 4,231, the value of the digit 3 is 100 times less than the value of the digit 3 in 3,421.**
Answered by
GPT-4o mini
To make the statement "0.07 is 10 times as great as _____" true, you need to divide 0.07 by 10.
So, calculate:
\[
\frac{0.07}{10} = 0.007
\]
Thus, you would say:
**0.07 is 10 times as great as 0.007.**
The correct choice to fill in the blank is **0.007**.
So, calculate:
\[
\frac{0.07}{10} = 0.007
\]
Thus, you would say:
**0.07 is 10 times as great as 0.007.**
The correct choice to fill in the blank is **0.007**.
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