Question
multiply 4.82x10^12 and 3.2x10^4
Answers
GPT-4o mini
To multiply \( 4.82 \times 10^{12} \) and \( 3.2 \times 10^{4} \), you can follow these steps:
1. Multiply the coefficients (the numbers in front):
\[
4.82 \times 3.2 = 15.424
\]
2. Add the exponents of 10:
\[
10^{12} \times 10^{4} = 10^{12 + 4} = 10^{16}
\]
3. Combine the results:
\[
15.424 \times 10^{16}
\]
For scientific notation, we typically express the coefficient as a number between 1 and 10. Therefore, we need to convert \( 15.424 \) to scientific notation:
\[
15.424 = 1.5424 \times 10^{1}
\]
Now combine this with the \( 10^{16} \):
\[
1.5424 \times 10^{1} \times 10^{16} = 1.5424 \times 10^{17}
\]
Thus, the final result is:
\[
\boxed{1.5424 \times 10^{17}}
\]
1. Multiply the coefficients (the numbers in front):
\[
4.82 \times 3.2 = 15.424
\]
2. Add the exponents of 10:
\[
10^{12} \times 10^{4} = 10^{12 + 4} = 10^{16}
\]
3. Combine the results:
\[
15.424 \times 10^{16}
\]
For scientific notation, we typically express the coefficient as a number between 1 and 10. Therefore, we need to convert \( 15.424 \) to scientific notation:
\[
15.424 = 1.5424 \times 10^{1}
\]
Now combine this with the \( 10^{16} \):
\[
1.5424 \times 10^{1} \times 10^{16} = 1.5424 \times 10^{17}
\]
Thus, the final result is:
\[
\boxed{1.5424 \times 10^{17}}
\]
bigepic
divide 4820000000000 and 32000
GPT-4o mini
To divide \( 4,820,000,000,000 \) by \( 32,000 \), you can perform the calculation directly.
1. Write the division:
\[
\frac{4,820,000,000,000}{32,000}
\]
2. Simplify the numbers. You can cancel out the thousands from the numerator and the denominator:
\[
\frac{4,820,000,000 \text{ (12 zeros)}}{32 \text{ (4 zeros)}} = \frac{4,820,000,000}{32}
\]
3. Now perform the division:
\[
4,820,000,000 \div 32 = 150,625,000
\]
So, the result of dividing \( 4,820,000,000,000 \) by \( 32,000 \) is:
\[
\boxed{150625000}
\]
1. Write the division:
\[
\frac{4,820,000,000,000}{32,000}
\]
2. Simplify the numbers. You can cancel out the thousands from the numerator and the denominator:
\[
\frac{4,820,000,000 \text{ (12 zeros)}}{32 \text{ (4 zeros)}} = \frac{4,820,000,000}{32}
\]
3. Now perform the division:
\[
4,820,000,000 \div 32 = 150,625,000
\]
So, the result of dividing \( 4,820,000,000,000 \) by \( 32,000 \) is:
\[
\boxed{150625000}
\]
bigepic
the denseity of oxygen is 0.001429 grams per cubic cm. how is this number written in scientific notation?
GPT-4o mini
To convert the density of oxygen, which is \( 0.001429 \) grams per cubic centimeter, into scientific notation, follow these steps:
1. Move the decimal point to the right until you have a number between 1 and 10. In this case, move the decimal point three places to the right:
\[
0.001429 \quad \text{becomes} \quad 1.429
\]
2. Count how many places you moved the decimal point. Here, the decimal was moved 3 places to the right, so we will use a negative exponent for the base 10:
\[
0.001429 = 1.429 \times 10^{-3}
\]
Therefore, the density of oxygen in scientific notation is:
\[
\boxed{1.429 \times 10^{-3}} \text{ grams per cubic cm.}
\]
1. Move the decimal point to the right until you have a number between 1 and 10. In this case, move the decimal point three places to the right:
\[
0.001429 \quad \text{becomes} \quad 1.429
\]
2. Count how many places you moved the decimal point. Here, the decimal was moved 3 places to the right, so we will use a negative exponent for the base 10:
\[
0.001429 = 1.429 \times 10^{-3}
\]
Therefore, the density of oxygen in scientific notation is:
\[
\boxed{1.429 \times 10^{-3}} \text{ grams per cubic cm.}
\]