Math 8 A Compare Very Large and Very Small Numbers Practice

Question

1. Use scientific notation to determine which of these numbers is greater: 34,835,760 or 43,835,760. Write your answer in scientific notation, expressed to the exact decimal place.
2. Use scientific notation to determine which of these numbers has the least value: 123,893,31,892 or 12,786. Write your answer in scientific notation, expressed to the exact decimal place.
3. Use scientific notation to determine which of these numbers has the greatest value: 654,987,034; 645,897,430; or 546,789,340. Write your answer in scientific notation, expressed to the exact decimal place.
4. Compare 0.0000635 and 0,000456. Write <, >, or = in the blank.
5. Which symbol makes the statement true? Write <, >, or = in the blank.

5 x 10^-11 {blank} 3 x 10^-11

Answer 1

Let's solve each of the problems one by one.

1. To express the numbers 34,835,760 and 43,835,760 in scientific notation:

   • 34,835,760 = 3.483576 × 10^7
   • 43,835,760 = 4.383576 × 10^7

   Comparing the coefficients (3.483576 vs 4.383576), we find that:

   • 4.383576 > 3.483576

   Therefore, the greater number is 4.383576 × 10^7.

2. To express the numbers 123,893,318,892 and 12,786 in scientific notation:

   • 123,893,318,892 = 1.23893318892 × 10^11
   • 12,786 = 1.2786 × 10^4

   Comparing the exponents (11 vs 4), since 10^11 is much larger than 10^4:

   • 1.23893318892 × 10^11 is much greater than 1.2786 × 10^4

   So, the number with the least value is 1.2786 × 10^4.

3. To express the numbers 654,987,034; 645,897,430; and 546,789,340 in scientific notation:

   • 654,987,034 = 6.54987034 × 10^8
   • 645,897,430 = 6.45897430 × 10^8
   • 546,789,340 = 5.46789340 × 10^8

   Comparing the coefficients:

   • 6.54987034 > 6.45897430 > 5.46789340

   Therefore, the greatest number is 6.54987034 × 10^8.

4. Now, comparing 0.0000635 and 0.000456 in scientific notation:

   • 0.0000635 = 6.35 × 10^-5
   • 0.000456 = 4.56 × 10^-4

   When comparing the exponents (-5 and -4), -4 is greater than -5, so:

   • 4.56 × 10^-4 > 6.35 × 10^-5

   Thus, the comparison is: 0.0000635 < 0.000456.

5. Comparing 5 x 10^-11 and 3 x 10^-11:

   • The exponents are the same (-11), so we can compare the coefficients:
   • 5 > 3

   Therefore, the correct symbol is: 5 x 10^-11 > 3 x 10^-11.

In summary:

1. 4.383576 × 10^7
2. 1.2786 × 10^4
3. 6.54987034 × 10^8
4. <

Answer 2

Bot is right as of 8:06 PM 9/23/2024

Thank you Bot!

Answer 3

You're welcome! I'm glad I could help. If you have any more questions or need assistance with anything else, feel free to ask. Have a great day!

Answer 4

Bot is correct on 11/9/24!! (Number five is >)