Which of the following is not a true statement?
A. 2 × 10⁶ is 10 times as great as 2 × 10⁵
B. 4 × 10⁸ is 100 time as great as 4 × 10⁶
C. 9 × 10^-4 is 1,000 times as great as 9 × 10^-7
D. 7 × 10^-2 is 1,000 times as great as 7 × 10^-6
B. 4 × 10⁸ is 100 time as great as 4 × 10⁶
To determine which of the statements is not true, we can compare the given values.
A. 2 × 10⁶ is 10 times as great as 2 × 10⁵
To verify this, we can divide 2 × 10⁶ by 2 × 10⁵:
(2 × 10⁶) / (2 × 10⁵) = 10
This statement is true.
B. 4 × 10⁸ is 100 times as great as 4 × 10⁶
Again, we can divide 4 × 10⁸ by 4 × 10⁶:
(4 × 10⁸) / (4 × 10⁶) = 100
This statement is also true.
C. 9 × 10^-4 is 1,000 times as great as 9 × 10^-7
Let's divide 9 × 10^-4 by 9 × 10^-7:
(9 × 10^-4) / (9 × 10^-7) = (9/9) × 10^(-4 - (-7)) = 10³ = 1000
This statement is true.
D. 7 × 10^-2 is 1,000 times as great as 7 × 10^-6
Now, let's perform the division 7 × 10^-2 by 7 × 10^-6:
(7 × 10^-2) / (7 × 10^-6) = (7/7) × 10^(-2 - (-6)) = 10^4 = 10,000
Therefore, the answer is D. 7 × 10^-2 is NOT 1,000 times as great as 7 × 10^-6.
To determine which of the statements is not true, let's analyze each one:
A. 2 × 10⁶ is 10 times as great as 2 × 10⁵.
To compare these two numbers, we can rewrite them in expanded form:
2 × 10⁶ = 2,000,000 and 2 × 10⁵ = 200,000.
Now, let's check if 2,000,000 is indeed 10 times as great as 200,000.
To find out, we divide 2,000,000 by 200,000: 2,000,000 ÷ 200,000 = 10.
B. 4 × 10⁸ is 100 times as great as 4 × 10⁶.
Again, let's rewrite these numbers in expanded form:
4 × 10⁸ = 400,000,000 and 4 × 10⁶ = 4,000,000.
Now, let's check if 400,000,000 is 100 times as great as 4,000,000.
To find out, we divide 400,000,000 by 4,000,000: 400,000,000 ÷ 4,000,000 = 100.
C. 9 × 10^-4 is 1,000 times as great as 9 × 10^-7.
Again, let's rewrite these numbers in expanded form:
9 × 10^-4 = 0.0009 and 9 × 10^-7 = 0.0000009.
Now, let's check if 0.0009 is 1,000 times as great as 0.0000009.
To find out, we divide 0.0009 by 0.0000009: 0.0009 ÷ 0.0000009 = 1,000.
D. 7 × 10^-2 is 1,000 times as great as 7 × 10^-6.
Again, let's rewrite these numbers in expanded form:
7 × 10^-2 = 0.07 and 7 × 10^-6 = 0.000007.
Now, let's check if 0.07 is 1,000 times as great as 0.000007.
To find out, we divide 0.07 by 0.000007: 0.07 ÷ 0.000007 = 10,000.
Based on our calculations, we can see that statement D is not true. The value 7 × 10^-2 is not 1,000 times as great as 7 × 10^-6. Instead, it is 10,000 times as great. Therefore, the answer is D.
Less than, greater than or equal to?
1. 8.341 × 10^-6 □ 2.15 × 10^-2
2. 1.98 × 10⁵ □ 8.91 × 10⁵
3. 2.14 × 10⁵ □ 2.14 × 10³
1. 8.341 × 10^-6 < 2.15 × 10^-2. (Less than)
2. 1.98 × 10⁵ < 8.91 × 10⁵. (Less than)
3. 2.14 × 10⁵ = 2.14 × 10³. (Equal to)