Compare very large and very small numbers Quick check
Question
Compare 364,879; 463,000; and 436,765 using scientific notation. Which number has the least value?3.64879 ×10^5
Use scientific notation to compare these numbers: 12,740,876,635; 1,345,763,334; and 12,920,370,000, which has the greatest value?
1.292037×10^10
Compare 7.6 × 10−25
and 6.7 × 10−52
. Which statement is true?
7.6 × 10−25 > 6.7 × 10−52
Which set of numbers is arranged in descending order?
7.6 × 10−25 , 7.2 × 10−25, 7.2 × 10−30, 7 × 10−30
In which set are the numbers arranged in ascending order?
3.25 × 10−4, 1.25 × 10−3, 2.25 × 10−3, 3.25 × 10−3
HOPE THIS HELP IF IT DIDN'T LET ME KNOW IN THE COMMENTS! AND I WILL TRY AND HELP YOU
The answers to the comparisons are as follows:
1. The number with the least value is 364,879 (3.64879 × 10^5).
2. The number with the greatest value is 12,920,370,000 (1.292037 × 10^10).
3. The statement "7.6 × 10−25 > 6.7 × 10−52" is true.
4. The numbers arranged in descending order are: 7.6 × 10−25, 7.2 × 10−25, 7.2 × 10−30, 7 × 10−30.
5. The numbers arranged in ascending order are: 3.25 × 10−4, 1.25 × 10−3, 2.25 × 10−3, 3.25 × 10−3.
Comparing very large and very small numbers using scientific notation:
1. Compare 364,879; 463,000; and 436,765:
- Convert the numbers to scientific notation:
364,879 = 3.64879 × 10^5
463,000 = 4.63 × 10^5
436,765 = 4.36765 × 10^5
- The number with the least value is 3.64879 × 10^5.
2. Compare 12,740,876,635; 1,345,763,334; and 12,920,370,000:
- Convert the numbers to scientific notation:
12,740,876,635 = 1.2740876635 × 10^10
1,345,763,334 = 1.345763334 × 10^9
12,920,370,000 = 1.292037 × 10^10
- The number with the greatest value is 1.292037 × 10^10.
3. Compare 7.6 × 10^−25 and 6.7 × 10^−52:
- The exponent -25 is greater than -52, so 7.6 × 10^−25 is greater than 6.7 × 10^−52.
4. Arrange the numbers in descending order: 7.6 × 10^−25, 7.2 × 10^−25, 7.2 × 10^−30, 7 × 10^−30
- The numbers arranged in descending order are: 7.6 × 10^−25, 7.2 × 10^−25, 7.2 × 10^−30, 7 × 10^−30.
5. Arrange the numbers in ascending order: 3.25 × 10^−4, 1.25 × 10^−3, 2.25 × 10^−3, 3.25 × 10^−3
- The numbers arranged in ascending order are: 3.25 × 10^−4, 1.25 × 10^−3, 2.25 × 10^−3, 3.25 × 10^−3.
I hope this helps! Let me know if you have any further questions.
To compare very large and very small numbers in scientific notation, you need to look at the coefficient (the number before the "x 10") and the exponent (the number after the "x 10").
In the first question, compare 364,879; 463,000; and 436,765 using scientific notation:
1. Convert each number to scientific notation:
364,879 = 3.64879 × 10^5
463,000 = 4.63 × 10^5
436,765 = 4.36765 × 10^5
2. Comparing the coefficients (the numbers before "x 10"), we see that 3.64879 is the smallest. Therefore, 3.64879 × 10^5 has the least value.
In the second question, compare 12,740,876,635; 1,345,763,334; and 12,920,370,000 using scientific notation:
1. Convert each number to scientific notation:
12,740,876,635 = 1.2740876635 × 10^10
1,345,763,334 = 1.345763334 × 10^9
12,920,370,000 = 1.292037 × 10^10
2. Comparing the coefficients, we see that 1.292037 × 10^10 has the largest coefficient. Therefore, 1.292037 × 10^10 has the greatest value.
In the third question, compare 7.6 × 10^-25 and 6.7 × 10^-52:
1. Both numbers are already in scientific notation, so no conversion is needed.
2. Comparing the exponents, we see that 10^-25 is bigger than 10^-52. Therefore, 7.6 × 10^-25 is greater than 6.7 × 10^-52.
In the fourth question, compare 7.6 × 10^-25, 7.2 × 10^-25, 7.2 × 10^-30, 7 × 10^-30 in descending order:
1. Comparing the coefficients, we see that 7.6 is the largest, followed by 7.2, then 7.
2. Within each coefficient, comparing the exponents, we see that 10^-25 is larger than 10^-30.
3. The descending order is: 7.6 × 10^-25, 7.2 × 10^-25, 7.2 × 10^-30, 7 × 10^-30.
In the fifth question, compare 3.25 × 10^-4, 1.25 × 10^-3, 2.25 × 10^-3, 3.25 × 10^-3 in ascending order:
1. Comparing the coefficients, we see that 3.25 is the smallest, followed by 1.25, then 2.25, and finally 3.25.
2. Within each coefficient, comparing the exponents, we see that 10^-4 is smaller than 10^-3.
3. The ascending order is: 3.25 × 10^-4, 1.25 × 10^-3, 2.25 × 10^-3, 3.25 × 10^-3.
Remember, when comparing numbers in scientific notation, start by comparing the coefficients and then compare the exponents if needed.