*This is orders of magnitude*
1)So, I have to estimate 16,700,000,000,000,000 the product of a single digit of 10.
- 2 x 10^16
- 2 x 10^15 *my answer*
- 1 x 10^16
- 1 x 10^15
2)0.00000394 estimated as the product of a single digit.
____ x 10____ *fill in the blanks* *my answer 3.94 x 10^6
3)Finding numbers are greater than 3 × 10^−7?
- 9 * 10^-9 *my answer*
- 2 x 10^-5
- 6 x 10^-7 *my answer*
- 5 x 10^-8
- 2 x 10^-7
4) best order of magnitude for 58,000
- 10^3 *my answer*
- 10^4
- 10^5
- 10^6
5)best order of magnitude estimate for 0.00003?
- 10^-3
- 10^-4
- 10^-5 *my answer*
- 10^-6
~I am having a difficult time with these problems! Please help, thanks!
No worries! I'll help you go through each problem step by step and explain how to find the correct answer.
1) So, to estimate the product of a single digit of 10, you need to determine the value of that digit. In this case, the number is 16,700,000,000,000,000. We know that 10 is raised to the power of 16, so the single digit will be 2. Therefore, the estimated product is 2 x 10^16.
2) For this problem, the number is 0.00000394. To estimate it as the product of a single digit, you need to move the decimal point to the right until you have only one non-zero digit to the left of the decimal point. In this case, you need to move the decimal point 6 places to the right, which gives you 3.94. Therefore, the estimated product is 3.94 x 10^6.
3) To find numbers greater than 3 x 10^-7, you need to compare the given options. In this case, the options are 9 x 10^-9, 2 x 10^-5, 6 x 10^-7, 5 x 10^-8, and 2 x 10^-7. Among these options, the only number greater than 3 x 10^-7 is 6 x 10^-7. Therefore, the correct answer is 6 x 10^-7.
4) The number given is 58,000. To determine the best order of magnitude, you need to find the power of 10 that is closest to the number. In this case, 10^3 is the closest power of 10 to 58,000 since it is equal to 1,000. Therefore, the correct answer is 10^3.
5) The number given is 0.00003. Similarly to problem 2, you need to move the decimal point to the right until you have only one non-zero digit to the left of the decimal point. In this case, you need to move the decimal point 5 places to the right, which gives you 3. Therefore, the estimated product is 3 x 10^-5.
I hope this helps! Let me know if you have any further questions.