Which of the following is not a true statement?
4 × 10^8 is 100 times as great as 4 x 10^6
2 × 10^6 is 10 times as great as 2 x 10^5
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
9 × 10^-4 is 1,000 times as great as 9 × 10^-7 is not a true statement.
wrong
Apologies for the incorrect response. The statement "7 × 10^-2 is 1,000 times as great as 7 × 10^-6" is not true.
can you explain?
Certainly!
To determine if a statement is true or not, we can compare the exponents and coefficients of the given numbers.
Let's start with the first statement:
4 × 10^8 is 100 times as great as 4 × 10^6.
Here, the exponents are equal (8 and 6). To compare the coefficients, we divide 4 × 10^8 by 4 × 10^6:
(4 × 10^8) / (4 × 10^6) = (4 / 4) × (10^8 / 10^6) = 1 × 10^2 = 100
Since the result is 100, the statement is true.
Now, consider the second statement:
2 × 10^6 is 10 times as great as 2 × 10^5.
Again, the exponents are equal (6 and 5). Dividing 2 × 10^6 by 2 × 10^5:
(2 × 10^6) / (2 × 10^5) = (2 / 2) × (10^6 / 10^5) = 1 × 10 = 10
The result is 10, confirming that the statement is true.
Next, let's analyze the third statement:
9 × 10^-4 is 1,000 times as great as 9 × 10^-7.
The exponents are different (-4 and -7). To compare the coefficients, we divide 9 × 10^-4 by 9 × 10^-7:
(9 × 10^-4) / (9 × 10^-7) = (9 / 9) × (10^-4 / 10^-7) = 1 × 10^3 = 1,000
This result demonstrates that the statement is true.
Lastly, we evaluate the fourth statement:
7 × 10^-2 is 1,000 times as great as 7 × 10^-6.
The exponents are distinct (-2 and -6). Dividing 7 × 10^-2 by 7 × 10^-6:
(7 × 10^-2) / (7 × 10^-6) = (7 / 7) × (10^-2 / 10^-6) = 1 × 10^4 = 10,000
The outcome of 10,000 shows that the statement is not true.
Therefore, the statement "7 × 10^-2 is 1,000 times as great as 7 × 10^-6" is not accurate.