Order of Magnitude (I'm not quite understanding it)

1) trying to 0.0000000734 estimated as the product with a single digit power of 10.*No multiple choice*

2) Trying to find the numbers that a greater than 7 x 10^-4 (Choose more than one answer type question)
- 8 x 10^-4 * my answer
- 9 x 10^-5 * my answer
- 4 x 10^-4
- 3 x 10^-2
- 7 x 10^-5 * my answer
3) best order of magnitude estimate for 29,300
- 10^4 * my answer
- 10^5
- 10^6
- 10^7
4) the best order of magnitude estimate for 0.0008
- 10^-3
- 10^-4 * my answer
- 10^-5
- 10^-6
Thanks! It's confusing to me :/

Online, “*” is used to indicate multiplication to avoid confusion with “x” as an unknown.

1) 7.34 * 10^-8

2) I assume the dashes in front of your choices are not meant to be negative signs.
10^-3 = .001
10^-4 = .0001
10^-5 = .00001
That should help you to choose.

3) Right

4) Right

.00000001

0.0000000734

Order of magnitude is a way to approximate the size or scale of a number by expressing it as a power of 10. It helps us understand the relative size of numbers without needing to know the exact value. The order of magnitude of a number is determined by counting the number of digits (excluding leading zeros) before the decimal point and representing it as a power of 10.

Now, let's go through each question and find the order of magnitude estimates.

1) To estimate 0.0000000734, we need to move the decimal point to create a number between 1 and 10. We can do this by multiplying it with a power of 10.

To determine the power of 10, count the number of decimal places you need to move the decimal point to the right to make it greater than or equal to 1. In this case, we need to move the decimal point to the right 7 places, so the power of 10 will be 10^7.

Therefore, the order of magnitude estimate for 0.0000000734 is 10^7.

2) To find the numbers greater than 7 x 10^-4, we need to look at the given choices.

- 8 x 10^-4 is greater than the given number.
- 9 x 10^-5 is smaller than the given number.
- 4 x 10^-4 is greater than the given number.
- 3 x 10^-2 is much larger than the given number.
- 7 x 10^-5 is smaller than the given number.

So, the numbers greater than 7 x 10^-4 are 8 x 10^-4 and 4 x 10^-4.

3) The best order of magnitude estimate for 29,300 is determined by counting the number of digits before the decimal point. In this case, there are four digits, so the order of magnitude estimate will be 10^4.

Therefore, the best order of magnitude estimate for 29,300 is 10^4.

4) The best order of magnitude estimate for 0.0008 is determined by counting the number of decimal places after the leading zeros. In this case, there are four decimal places, so the order of magnitude estimate will be 10^-4.

Therefore, the best order of magnitude estimate for 0.0008 is 10^-4.

I hope this explanation clears up the concept of order of magnitude for you!