1. Which of the following expressions is written in scientific notation?

1. 73.4 x 105
2. 0.09 × 107
3. 80 x 103
4. 4.22 x 10–3

2. Which of the following is 0.0000000708 written in scientific notation?
1. 7.08 x 10–8
2. 7.8 x 10–8
3. 708 x 10–10
4. 70.08 x 10–9

3. Which expression represents the largest number?
1. 40.1 x 10–6
2. 4.1 x 10–7
3. 0.411 x 10–7
4. 0.04001 x 10–5
4. Which expression is equal to 1/8000 written in scientific notation?

1. 8.0 x 103
2. 1.25 x 10–4
3. 125 x 10–5
4. 1.25 x 104

1. The expression written in scientific notation is 4.22 x 10–3 (Option 4).

2. To determine the scientific notation for 0.0000000708, we need to move the decimal point to the right until there is a single non-zero digit to the left. Count the number of places the decimal point was moved. The correct expression would be 7.08 x 10–8 (Option 1).

3. To compare the expressions and find the largest number, we need to convert them to standard form.
- Option 1: 40.1 x 10–6 = 0.0000401
- Option 2: 4.1 x 10–7 = 0.00000041
- Option 3: 0.411 x 10–7 = 0.0000000411
- Option 4: 0.04001 x 10–5 = 0.0000004001

The largest number is represented by Option 1, 40.1 x 10–6.

4. To express 1/8000 in scientific notation, we need to find the decimal point position for a non-zero digit to the left of 1. Since 1/8000 is a small number, the decimal point needs to be moved to the left. It can be expressed as 1.25 x 10–4 (Option 2).

1. To determine which expression is written in scientific notation, we need to look for a number that is written in the form of "a x 10^b" where "a" is a number between 1 and 10, and "b" is an integer. Let's analyze each expression:

1. 73.4 x 10^5: This expression is in scientific notation because it follows the format "a x 10^b" with "a" being 73.4 and "b" being 5. So, the answer is option 1.

2. 0.09 x 10^7: This expression is not in scientific notation because the number "a" is less than 1. It should be written as 9 x 10^-2 to be in scientific notation.

3. 80 x 10^3: This expression is not in scientific notation because the number "a" is greater than 10. It should be written as 8 x 10^4 to be in scientific notation.

4. 4.22 x 10^-3: This expression is in scientific notation because it follows the format "a x 10^b" with "a" being 4.22 and "b" being -3. So, the answer is option 4.

Therefore, the correct answer is option 1.

2. We have the number 0.0000000708 and we need to write it in scientific notation. To do that, we must move the decimal point to the right until there is only one non-zero digit to the left of the decimal point. The number of places we moved the decimal point is the exponent.

0.0000000708 can be written as 7.08 x 10^-8.

So, the correct answer is option 1.

3. To determine which expression represents the largest number, we need to compare the coefficients (the numbers "a") of each expression. The exponent (the number "b") does not affect the comparison because it only represents the magnitude of the number.

Let's compare the coefficients of each expression:

1. 40.1 x 10^-6
2. 4.1 x 10^-7
3. 0.411 x 10^-7
4. 0.04001 x 10^-5

By comparing the coefficients, we can see that option 1 has the largest coefficient (40.1). Therefore, the correct answer is option 1.

4. We have the fraction 1/8000 and we need to write it in scientific notation.

To convert a fraction to scientific notation, we need to write the numerator (1) and denominator (8000) as numbers between 1 and 10 by moving the decimal point. Then, the denominator is converted to a power of 10.

1/8000 can be written as 1.25 x 10^-4. (1/8000 = 0.000125 = 1.25 x 10^-4)

So, the correct answer is option 2.

A number written in scientific notation has to be between 1 and 10. The 10 to whatever power tells you whether to move the decimal point right or left depending on whether it is positive or negative. So for number one, the answer has to be 4. The actual number is 0.0042 because the decimal moves 3 places to the left since it is a -3.