Which of the following is not a true statement four times 10 to the power of 8 is 100 * as great as 4 * 10 ^ 6 7 * 10 ^ -2 is a thousand times as great as 7 * 10 ^ -6 2 * 10 ^ 6 is 10 times as great as 2 to the times 10 to the power of 5 9 * 10 ^ -4 is a thousand times as great as 9 * 10 ^ -7
The statement "2 * 10 ^ 6 is 10 times as great as 2 to the times 10 to the power of 5" is not true.
To determine which statement is not true, we need to evaluate each statement individually and compare the quantities. Let's break down each statement:
1. Four times 10 to the power of 8 is 100 times as great as 4 times 10 to the power of 6.
To compare the quantities, we can simplify both sides by dividing them with 100:
(4 * 10^8)/100 = 4 * 10^6
This shows that both sides are equal, so the statement is true.
2. 7 times 10 to the power of -2 is a thousand times as great as 7 times 10 to the power of -6.
To compare the quantities, we can simplify both sides by multiplying them with 1000:
7 * 10^(-2) * 1000 = 7 * 10^(-6)
This shows that both sides are equal, so the statement is true.
3. 2 times 10 to the power of 6 is 10 times as great as 2 to the power of 10 to the power of 5.
To compare the quantities, let's first evaluate 2 to the power of 5:
2^5 = 32
Now, let's calculate the left side of the statement:
2 * 10^6 = 2,000,000
Comparing the quantities, we see that 2,000,000 is not equal to 32. Therefore, the statement is not true.
4. 9 times 10 to the power of -4 is a thousand times as great as 9 times 10 to the power of -7.
To compare the quantities, we can simplify both sides by multiplying them with 1000:
9 * 10^(-4) * 1000 = 9 * 10^(-7)
This shows that both sides are equal, so the statement is true.
Based on the evaluation, the third statement is not true.
Let's analyze each statement and determine which one is not true.
Statement 1: Four times 10 to the power of 8 is 100 times as great as 4 times 10 to the power of 6.
To check if this statement is true, we can calculate both sides of the equation:
Four times 10 to the power of 8 = 4 * 10^8 = 400,000,000
And 100 times as great as 4 times 10 to the power of 6 = 100 * (4 * 10^6) = 400,000,000
Since both sides of the equation are equal, this statement is true.
Statement 2: 7 times 10 to the power of -2 is a thousand times as great as 7 times 10 to the power of -6.
To check if this statement is true, we can calculate both sides of the equation:
7 times 10 to the power of -2 = 7 * 10^(-2) = 0.07
And a thousand times as great as 7 times 10 to the power of -6 = 1000 * (7 * 10^(-6)) = 0.007
Since 0.07 is not equal to 0.007, this statement is not true.
Statement 3: 2 times 10 to the power of 6 is 10 times as great as 2 to the power of 10 to the power of 5.
To check if this statement is true, we can calculate both sides of the equation:
2 times 10 to the power of 6 = 2 * 10^6 = 2,000,000
And 10 times as great as 2 to the power of 10 to the power of 5 = 10 * (2 * 10^(10^5)) = 10 * (2 * 10^100000) = a very large number
Since 2,000,000 is not equal to a very large number, this statement is not true.
Statement 4: 9 times 10 to the power of -4 is a thousand times as great as 9 times 10 to the power of -7.
To check if this statement is true, we can calculate both sides of the equation:
9 times 10 to the power of -4 = 9 * 10^(-4) = 0.0009
And a thousand times as great as 9 times 10 to the power of -7 = 1000 * (9 * 10^(-7)) = 0.009
Since 0.0009 is not equal to 0.009, this statement is not true.
Therefore, the statement that is not true is statement number 2: "7 * 10^-2 is a thousand times as great as 7 * 10^-6."