Question

Write 0.0000000065 in scientific notation.
Answered by GPT-4o mini
The number 0.0000000065 in scientific notation is written as \( 6.5 \times 10^{-9} \).
Answer
the speed of light is about 671,000,000 miles per hour. How will you write this number in scientific notation?

a. 6.71 x 10^8
b. 6.71 x 10^-8
c. 6.71 x 10^-3
d. 6.71 x 10^3
Answered by GPT-4o mini
To write the speed of light, 671,000,000 miles per hour, in scientific notation, you first express it as \( 6.71 \) multiplied by a power of 10.

671,000,000 can be rewritten as \( 6.71 \times 10^8 \).

Thus, the correct choice is:

**a. \( 6.71 \times 10^8 \)**.
Answer
suppose an average person blinks 15 times per hour. how many times does an average person blink in a year? Write the answer in scientific notation (Hint: 1 year=365 days, 1 day = 24 hours).

a. 1.314 x 10^-5
b. 1.314 x 10^5
c. 1.314 x 10^-4
d. 1.314 x 10^4
Answered by GPT-4o mini
To calculate how many times an average person blinks in a year:

1. **Blinks per hour**: 15
2. **Hours per day**: 24
3. **Days per year**: 365

Now, compute the total number of blinks in a year:

\[
\text{Total blinks in a year} = 15 \, \text{blinks/hour} \times 24 \, \text{hours/day} \times 365 \, \text{days/year}
\]

Calculating this step by step:

\[
15 \, \text{blinks/hour} \times 24 \, \text{hours/day} = 360 \, \text{blinks/day}
\]

Then, multiply by the number of days in a year:

\[
360 \, \text{blinks/day} \times 365 \, \text{days/year} = 131,400 \, \text{blinks/year}
\]

Now write 131,400 in scientific notation:

\[
131,400 = 1.314 \times 10^5
\]

Thus, the correct answer is:

**b. \( 1.314 \times 10^5 \)**.
Answer
what is the number
5.9 x 10^5 written in decimal
notation?

a. 590,000
b. 5,9000,000
c. 5.90000
d. 0.000059
Answered by GPT-4o mini
To convert the scientific notation \( 5.9 \times 10^5 \) to decimal notation, you move the decimal point 5 places to the right (because of the positive exponent).

Starting with \( 5.9 \):

1. Move the decimal point 5 places to the right:
- Moving 1 place: \( 59.0 \)
- Moving 2 places: \( 590.0 \)
- Moving 3 places: \( 5900.0 \)
- Moving 4 places: \( 59000.0 \)
- Moving 5 places: \( 590000.0 \)

So, \( 5.9 \times 10^5 = 590,000 \).

The correct answer is:

**a. 590,000**.
Answer
what is the number
5.9 x 10^5 written in decimal
notation?

a. 730,000,000
b. 0.00000007.3
c. 0.0000000073
d. 0.000000073
Answered by GPT-4o mini
To convert \( 5.9 \times 10^5 \) into decimal notation, you move the decimal point 5 places to the right (because of the positive exponent).

Starting with \( 5.9 \):

1. Move the decimal point 5 places to the right:
- Moving 1 place: \( 59.0 \)
- Moving 2 places: \( 590.0 \)
- Moving 3 places: \( 5900.0 \)
- Moving 4 places: \( 59000.0 \)
- Moving 5 places: \( 590000.0 \)

Thus, \( 5.9 \times 10^5 = 590,000 \).

None of the provided options (\( a. 730,000,000 \), \( b. 0.00000007.3 \), \( c. 0.0000000073 \), \( d. 0.000000073 \)) correspond to \( 590,000 \).

Would you like to clarify if there are any corrections in the options given?
Answer
what is the number
7.3 x 10^-8 written in decimal
notation?

a. 730,000,000
b. 0.00000007.3
c. 0.0000000073
d. 0.000000073
Answered by GPT-4o mini
To convert \( 7.3 \times 10^{-8} \) into decimal notation, you move the decimal point 8 places to the left (because of the negative exponent).

Starting with \( 7.3 \):

1. Move the decimal point 1 place to the left: \( 0.73 \)
2. Move the decimal point 2 places to the left: \( 0.073 \)
3. Move the decimal point 3 places to the left: \( 0.0073 \)
4. Move the decimal point 4 places to the left: \( 0.00073 \)
5. Move the decimal point 5 places to the left: \( 0.000073 \)
6. Move the decimal point 6 places to the left: \( 0.0000073 \)
7. Move the decimal point 7 places to the left: \( 0.00000073 \)
8. Move the decimal point 8 places to the left: \( 0.000000073 \)

Thus, \( 7.3 \times 10^{-8} = 0.000000073 \).

The correct answer is:

**d. 0.000000073**.