Question

Which of the following is not a true statement?(1 point)
Responses

4 × 10^8 is 100 times as great as 4 × 106

9 × 10^−4 is 1,000 times as great as 9 × 10^−7

7 × 10^−2 is 1,000 times as great as 7 × 10^−6

2 × 10^6 is 10 times as great as 2 × 10^5

Answer 1

Let's evaluate each statement to determine which one is not true.

1. **4 × 10^8 is 100 times as great as 4 × 10^6**:
- \( 4 × 10^8 = 4 × 100000000 = 400000000 \)
- \( 4 × 10^6 = 4 × 1000000 = 4000000 \)
- To see if \( 4 × 10^8 \) is 100 times \( 4 × 10^6 \):
\[
100 × (4 × 10^6) = 100 × 4000000 = 400000000
\]
- This statement is true.

2. **9 × 10^−4 is 1,000 times as great as 9 × 10^−7**:
- \( 9 × 10^{-4} = 0.0009 \)
- \( 9 × 10^{-7} = 0.0000009 \)
- To check if \( 9 × 10^{-4} \) is 1,000 times \( 9 × 10^{-7} \):
\[
1000 × (9 × 10^{-7}) = 1000 × 0.0000009 = 0.0009
\]
- This statement is true.

3. **7 × 10^−2 is 1,000 times as great as 7 × 10^−6**:
- \( 7 × 10^{-2} = 0.07 \)
- \( 7 × 10^{-6} = 0.000007 \)
- Checking if \( 7 × 10^{-2} \) is 1,000 times \( 7 × 10^{-6} \):
\[
1000 × (7 × 10^{-6}) = 1000 × 0.000007 = 0.007
\]
- This means \( 0.07 \) is not equal to \( 0.007 \).
- Thus, this statement is **not true**.

4. **2 × 10^6 is 10 times as great as 2 × 10^5**:
- \( 2 × 10^{6} = 2000000 \)
- \( 2 × 10^{5} = 200000 \)
- Checking if \( 2 × 10^{6} \) is 10 times \( 2 × 10^{5} \):
\[
10 × (2 × 10^{5}) = 10 × 200000 = 2000000
\]
- This statement is true.

Therefore, the statement that is **not true** is:

**7 × 10^−2 is 1,000 times as great as 7 × 10^−6**.