Select all of the true statements. 4 × 10^2 is 0.04 times as much as 1 × 10^3 7 × 10^
-3 is 35 times as much as 2 × 10^-4 7 × 10^3 is 0.001 times as much as 7 × 10^5 3 × 10^-2 is 6 times as much as 5 × 10^-3
The true statements are:
- "4 × 10^2 is 0.04 times as much as 1 × 10^3."
- "7 × 10^-3 is 35 times as much as 2 × 10^-4."
- "7 × 10^3 is 0.001 times as much as 7 × 10^5."
- "3 × 10^-2 is 6 times as much as 5 × 10^-3."
To determine which statements are true, let's compare the values of each expression.
Statement 1: 4 × 10^2 is 0.04 times as much as 1 × 10^3.
To compare 4 × 10^2 and 1 × 10^3, we can re-write them as 400 and 1,000. Is 400 equal to 0.04 times 1,000? No. 0.04 times 1,000 is equal to 40, not 400. Therefore, this statement is false.
Statement 2: 7 × 10^-3 is 35 times as much as 2 × 10^-4.
To compare 7 × 10^-3 and 2 × 10^-4, we can re-write them as 0.007 and 0.0002. Is 0.007 equal to 35 times 0.0002? No. 35 times 0.0002 is equal to 0.007, not 0.007. Therefore, this statement is true.
Statement 3: 7 × 10^3 is 0.001 times as much as 7 × 10^5.
To compare 7 × 10^3 and 7 × 10^5, we can re-write them as 7,000 and 700,000. Is 7,000 equal to 0.001 times 700,000? No. 0.001 times 700,000 is equal to 700, not 7,000. Therefore, this statement is false.
Statement 4: 3 × 10^-2 is 6 times as much as 5 × 10^-3.
To compare 3 × 10^-2 and 5 × 10^-3, we can re-write them as 0.03 and 0.005. Is 0.03 equal to 6 times 0.005? Yes, 6 times 0.005 is indeed equal to 0.03. Therefore, this statement is true.
Summary:
Based on the comparison of values, statement 2 ("7 × 10^-3 is 35 times as much as 2 × 10^-4") and statement 4 ("3 × 10^-2 is 6 times as much as 5 × 10^-3") are true. Statements 1 and 3 are false.
To determine which statements are true, let's evaluate each one.
1) 4 × 10^2 is 0.04 times as much as 1 × 10^3.
To compare the two values, divide 4 × 10^2 by 1 × 10^3:
(4 × 10^2) / (1 × 10^3) = (4/1) × (10^2/10^3) = 4 × 10^-1 = 0.4
Since 0.4 is not equal to 0.04, this statement is false.
2) 7 × 10^-3 is 35 times as much as 2 × 10^-4.
To compare the two values, divide 7 × 10^-3 by 2 × 10^-4:
(7 × 10^-3) / (2 × 10^-4) = (7/2) × (10^-3/10^-4) = 3.5 × 10^1 = 35
Since 35 is equal to 35, this statement is true.
3) 7 × 10^3 is 0.001 times as much as 7 × 10^5.
To compare the two values, divide 7 × 10^3 by 7 × 10^5:
(7 × 10^3) / (7 × 10^5) = (7/7) × (10^3/10^5) = 0.001
Since 0.001 is equal to 0.001, this statement is true.
4) 3 × 10^-2 is 6 times as much as 5 × 10^-3.
To compare the two values, divide 3 × 10^-2 by 5 × 10^-3:
(3 × 10^-2) / (5 × 10^-3) = (3/5) × (10^-2/10^-3) = 0.6
Since 0.6 is not equal to 6, this statement is false.
Therefore, the true statements are:
- 7 × 10^-3 is 35 times as much as 2 × 10^-4.
- 7 × 10^3 is 0.001 times as much as 7 × 10^5.