compare very large and very small numbers quick check answers
Comparing very large and very small numbers can be done by looking at their magnitudes or exponents. Here are the quick check answers:
1. Which number is larger: 10^9 or 1^12?
The number 1^12 is larger.
2. Which number is smaller: 3 x 10^6 or 7 x 10^4?
The number 7 x 10^4 is smaller.
3. Which number is larger: 5 x 10^-3 or 2 x 10^-2?
The number 2 x 10^-2 is larger.
4. Which number is smaller: 4 x 10^10 or 8 x 10^9?
The number 8 x 10^9 is smaller.
5. Which number is larger: 9 x 10^-6 or 1 x 10^-5?
The number 1 x 10^-5 is larger.
Comparing very large and very small numbers can be done using quick checks. Here are some quick check methods for comparing numbers:
1. Scientific notation: Express both the large and small numbers in scientific notation. For example, if we have 1.25 x 10^8 and 3.6 x 10^-6, we can compare the exponents first. The larger exponent indicates the larger number. In this case, 10^8 is larger than 10^-6, so 1.25 x 10^8 is larger than 3.6 x 10^-6.
2. Order of magnitude: Another way to compare large and small numbers is to consider their orders of magnitude. The order of magnitude is the power of 10 that represents the size of a number. For example, 1,000 is of higher magnitude than 100. If the difference in order of magnitudes is significant, it is likely that the number with the higher magnitude is larger.
3. Comparison based on place value: If the numbers are given in decimal form, you can compare them based on their place values. Start by comparing the digits in the leftmost place, then move to the right. If at any point the digits differ, you can determine which number is larger.
4. Ratio comparison: Take the ratio of the two numbers. If the ratio is greater than 1, the larger number is the numerator. If the ratio is less than 1, the smaller number is the numerator.
It is important to note that these quick checks may not give you an exact comparison but can provide a good estimate for large and small numbers.
To compare very large and very small numbers, you can use scientific notation. Scientific notation represents numbers as a product of a decimal number and a power of 10.
Let's consider an example with two numbers: 2.4 x 10^8 and 3.6 x 10^-4.
To compare these numbers, follow these steps:
1. Compare the powers of 10: In this case, the first number has a power of 10 raised to 8, while the second number has a power of 10 raised to -4. Since 8 is greater than -4, the number with the larger exponent is larger.
2. If the powers of 10 are the same, compare the decimal numbers: Since the powers of 10 are not the same in our example, we don't need to do this step.
Based on the comparison of the powers of 10, we can conclude that 2.4 x 10^8 is larger than 3.6 x 10^-4.
By using scientific notation, we make it easier to compare very large and very small numbers because we mainly focus on the exponent of 10 to determine the magnitudes of the numbers.