Decide whether each statement is true. Choose Yes or No from the drop-down box.

Question

3×10×10×10=3×103

Choose

400,000=4×106

Choose

7×105=7×100,000

Choose

5 × 1,000=5,000

Choose

Answer 1

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

Answer 2

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.

Answer 3

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.

Answer 4

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

Answer 5

The word form of the number 2,909 is two thousand nine hundred nine.

Part A Answer:

two thousand nine hundred nine

Answer 6

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)

Answer 7

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:

\[ (2 \times 1,000) + (9 \times 100) + (9 \times 1) \]

Answer 8

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.

Answer 9

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.

Answer 10

Select a number to make the following statement true.

(1 point)
0.07 is 10 times as great as
Choose
.

Answer 11

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.