How many times less is 10^2 than 10^6 ? Express your answer as an integer power of 10.(1 point)

Responses

10,000

10^−4

0.0001

10^4

The answer is 10^−4.

To determine how many times less 10^2 is than 10^6, we need to divide the larger number by the smaller number.

10^6 ÷ 10^2 = 10^(6-2) = 10^4

Therefore, 10^2 is 10^4 times less than 10^6.

To determine how many times less 10^2 is than 10^6, we can divide 10^6 by 10^2.

When dividing numbers with the same base, we subtract the exponents. In this case, we have 10^6 ÷ 10^2, which can be rewritten as 10^(6-2).

So, 10^(6-2) = 10^4.

Therefore, 10^2 is 10^4 times less than 10^6.

Answer: 10^4

Roughly, it takes light less than 0.000000003 of a second to travel a one-meter distance. Express this number in the form of a × 10^n where 1 < a < 10 and is a one-digit number.(1 point)

Responses

3 × 10^8
3 times 10 superscript 8 baseline

3 × 10^−8
3 times 10 superscript negative 8 baseline

3 × 109
3 times 10 superscript 9 baseline

3 × 10^−9
3 times 10 superscript negative 9 baseline

The answer is 3 × 10^−9.

Could you explain?

Certainly! To express a number in the form of a × 10^n, we want to write the number as a decimal between 1 and 10 multiplied by a power of 10.

In this case, we are given that it takes light less than 0.000000003 (or 3 × 10^-9) of a second to travel a one-meter distance.

So, the decimal part is 3, and the power of 10 is -9.

Therefore, we can express the number as 3 × 10^-9.