Question

which one is greater: 3.2x^-10 or 2.3x10^-12?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine which expression is greater, we need to compare the values of the expressions.

First, let's simplify the expressions:

3.2x^-10 = 3.2 / x^10
2.3x10^-12 = 2.3 * 10^-12

Since we don't have a specific value for x, we can still compare these expressions based on the constant values.

Comparing 3.2 / x^10 and 2.3 * 10^-12:

To compare these fractions, we need to have the same denominator. Let's multiply both expressions by x^10 to get a common denominator:

(3.2 / x^10) * (x^10 / x^10) = 3.2x^10 / x^10 = 3.2

So, the first expression 3.2x^-10 simplifies to 3.2.

Now, let's compare 3.2 and 2.3 * 10^-12:

Since 10^-12 is a very small number (a fraction less than 1), multiplying it by any positive number like 2.3 will result in an even smaller number.

Therefore, 2.3 * 10^-12 is smaller than 3.2.

Conclusion: The first expression 3.2x^-10 is greater than the second expression 2.3x10^-12.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To determine which number is greater between 3.2x^-10 and 2.3x10^-12, we'll compare the exponents.

First, let's compare the exponents without considering the coefficients:
-10 vs -12

Since -10 is greater than -12, the number 3.2x^-10 has a larger exponent than 2.3x10^-12.

Now, let's compare the coefficients:
3.2 vs 2.3

Since 3.2 is greater than 2.3, the number 3.2x^-10 has a larger coefficient than 2.3x10^-12.

Therefore, the number 3.2x^-10 is greater than 2.3x10^-12.

Answer 3

[AI-generated answer — Explain Bot]

To compare the given numbers, 3.2x^-10 and 2.3x10^-12, we first need to understand how to compare numbers written in scientific notation.

Scientific notation is a way to express numbers using a coefficient multiplied by a power of 10. The coefficient represents the significant digits, and the power of 10 determines the scale or magnitude of the number.

To compare numbers in scientific notation, we need to compare the coefficients first. If the coefficients are equal, then we compare the powers of 10. The number with the larger coefficient is greater, and if the coefficients are equal, the number with the smaller power of 10 is greater.

Let's compare the given numbers step by step:

Number 1: 3.2x^-10
Coefficient 1: 3.2
Power of 10 1: -10

Number 2: 2.3x10^-12
Coefficient 2: 2.3
Power of 10 2: -12

Comparing the coefficients:
3.2 is greater than 2.3, so Number 1 has a larger coefficient.

Since the coefficients are different, we can conclude that Number 1 (3.2x^-10) is greater than Number 2 (2.3x10^-12).

Therefore, 3.2x^-10 is greater than 2.3x10^-12.