Compare Very Large and very small Numbers Quick Check
When comparing very large and very small numbers, there are a few key points to consider:
1. Magnitude: Very large numbers typically have a greater magnitude than very small numbers. For example, 1,000,000 is much larger than 0.000001.
2. Exponents: Very large numbers are usually expressed using positive exponents, while very small numbers are expressed using negative exponents. For example, 10^6 represents a large number, whereas 10^-6 represents a small number.
3. Decimal Point: Very large numbers often have the decimal point moved to the right, indicating a greater number of digits before the decimal point. Very small numbers have the decimal point moved to the left, indicating a greater number of digits after the decimal point.
4. Units: Very large numbers may be used to represent quantities like population, GDP, or distances in light-years. Very small numbers may represent quantities like atomic size, electron volts, or error tolerances.
When comparing very large and very small numbers, it is important to keep these factors in mind to fully understand their scale and significance.
What does descending mean
Descending means arranging in a decreasing or reverse order. When a list or set of numbers is arranged in descending order, the largest value comes first, followed by the second-largest value, and so on, with the smallest value coming last. This is the opposite of ascending order, where the values are arranged in increasing order. For example, if we have a set of numbers {5, 8, 2, 10, 3}, arranging them in descending order would result in {10, 8, 5, 3, 2}.
In which set are the numbers arranged in ascending order?(1 point)
a. 3.25 × 10−3, 2.25 × 10−3, 3.25 × 10−4, 1.25 × 10−3
b. 0.000325, 0.00225, 0.00125, 0.00325
c. 3.25 × 10−4, 1.25 × 10−3, 2.25 × 10−3, 3.25 × 10−3
d. 0.00125, 0.00225, 0.000325, 0.00325
To determine which set is arranged in ascending order, we need to compare the numbers from smallest to largest.
Let's evaluate the options:
a. 3.25 × 10^−3, 2.25 × 10^−3, 3.25 × 10^−4, 1.25 × 10^−3
Here, the numbers arranged in ascending order would be: 3.25 × 10^−4, 2.25 × 10^−3, 1.25 × 10^−3, 3.25 × 10^−3
But this is not the given order, so option a is not in ascending order.
b. 0.000325, 0.00225, 0.00125, 0.00325
Here, the numbers are already in ascending order, starting with the smallest: 0.000325, 0.00125, 0.00225, 0.00325
So option b is arranged in ascending order.
c. 3.25 × 10^−4, 1.25 × 10^−3, 2.25 × 10^−3, 3.25 × 10^−3
Here, the numbers arranged in ascending order would be: 3.25 × 10^−4, 1.25 × 10^−3, 2.25 × 10^−3, 3.25 × 10^−3
But this is not the given order, so option c is not in ascending order.
d. 0.00125, 0.00225, 0.000325, 0.00325
Here, the numbers arranged in ascending order would be: 0.000325, 0.00125, 0.00225, 0.00325
But this is not the given order, so option d is not in ascending order.
After evaluating the options, we find that option b is the only one arranged in ascending order.
To compare very large and very small numbers, follow these steps:
1. Identify the magnitude: Determine whether the numbers are large or small. This will help you understand the scale of the numbers you are comparing.
2. Use scientific notation (if necessary): If the numbers are extremely large or extremely small, it may be more convenient to write them in scientific notation. This allows you to express them as a coefficient multiplied by a power of 10.
3. Compare the coefficients: Look at the numbers before the power of 10. Determine which number is larger or smaller based on these coefficients. Ignore the power of 10 for now.
4. Account for the power of 10: If the coefficients are the same, compare the power of 10. A larger power of 10 indicates a larger number, while a smaller power of 10 indicates a smaller number.
5. Finalize the comparison: Combine the comparison of the coefficients and the power of 10 to determine the final result. For example, if one number has a larger coefficient but a smaller power of 10, it may still be smaller overall.
Remember to consider the context and magnitude of the numbers you are comparing.
To compare very large and very small numbers, you can use scientific notation.
1. Write down both numbers in scientific notation. To do this, express each number as a coefficient multiplied by a power of 10. For example, if you have the number 1,000,000,000, you can write it as 1 x 10^9 in scientific notation.
2. Compare the exponents of the powers of 10. If the exponents are the same, focus on comparing the coefficients. The number with the larger coefficient is greater.
3. If the exponents are different, the number with the larger exponent is greater. This is because it indicates a greater number of zeros in the original non-scientific notation.
For example, let's compare 1 x 10^9 (1,000,000,000) and 1 x 10^-6 (0.000001):
- The exponents are different: 9 vs -6.
- Since 9 is greater than -6, the number with the larger exponent (1 x 10^9) is greater.
Remember, scientific notation is a useful way to compare large and small numbers because it simplifies the process by focusing on the exponents and coefficients separately.