1.
Write the number 4,500,000 in scientific notation.
Correct Answer
A. 4.5 x 10^6
Explanation
The correct answer is 4.5 x 10^6. Scientific notation is a way to express very large or very small numbers in a concise form. In this case, the number 4,500,000 is written as 4.5 multiplied by 10 raised to the power of 6, which represents moving the decimal point 6 places to the right.
2.
Check any of the following that are correctly in scientific notation:
Correct Answer(s)
C. 9.3 x 10^2
D. 4 x 10^13
E. 9.4 x 10^-12
Explanation
The given numbers are correctly written in scientific notation because they are written in the form of a decimal number between 1 and 10 multiplied by a power of 10. Specifically, 9.3 x 10^2 represents 930, 4 x 10^13 represents 4,000,000,000,000,000, and 9.4 x 10^-12 represents 0.0000000000094.
3.
What is the standard form for this?
3,500,000,000
Correct Answer
A. 3.5*10^9
Explanation
The given number, 3,500,000,000, can be expressed in standard form as 3.5 * 10^9. In standard form, a number is written as a decimal number between 1 and 10, multiplied by a power of 10. Here, the decimal number is 3.5, and it is multiplied by 10 raised to the power of 9, which represents the number of zeros in the original number.
4.
What is the scientific form for this?
9.4*10^8
Correct Answer
A. 940,000,000
Explanation
The scientific form of the given number is 9.4*10^8. In scientific notation, a number is expressed as a product of a decimal number between 1 and 10 and a power of 10. In this case, 9.4 is the decimal number and 10^8 represents multiplying 9.4 by 10 eight times. Therefore, the scientific form of 9.4*10^8 is 940,000,000.
5.
Write the number 4,500,000 in scientific notation.
Correct Answer
A. 4.5 x 10^6
Explanation
The correct answer is 4.5 x 10^6. In scientific notation, a number is expressed as a decimal between 1 and 10 multiplied by a power of 10. In this case, 4.5 is the decimal between 1 and 10, and it is multiplied by 10^6 to indicate that it needs to be multiplied by 1 million. So, 4.5 x 10^6 is the correct scientific notation for 4,500,000.
6.
Check any of the following that are correctly in scientific notation:
Correct Answer(s)
C. 9.3 x 10^2
D. 4 x 10^13
E. 9.4 x 10^-12
Explanation
The given answer correctly identifies the numbers that are written in scientific notation. Scientific notation is a way to express very large or very small numbers using powers of 10. In scientific notation, a number is written as a decimal between 1 and 10, multiplied by a power of 10. The numbers 9.3 x 10^2, 4 x 10^13, and 9.4 x 10^-12 all follow this format and are correctly written in scientific notation.
7.
What is the standard form for this?
3,500,000,000
Correct Answer
A. 3.5*10^9
Explanation
The standard form for the number 3,500,000,000 is 3.5*10^9. This is because in standard form, a number is written as a decimal number between 1 and 10, multiplied by a power of 10. In this case, 3.5 is the decimal number and 10^9 represents 10 raised to the power of 9, which means the number is multiplied by 10 nine times.
8.
What is the scientific form for this?
9.4*10^8
Correct Answer
A. 940,000,000
Explanation
The scientific form for the given number is 9.4 * 10^8. In scientific notation, a number is expressed as a product of a decimal number between 1 and 10, multiplied by a power of 10. In this case, 9.4 is the decimal number and 10^8 represents a power of 10. The exponent 8 indicates that the decimal point should be moved 8 places to the right, resulting in 940,000,000.
9.
Is the following numbers in proper scientific notation? 23.2 x 10^{2}
Correct Answer
B. No, this is not proper scientific notation
Explanation
2.32 x 10^3
10.
Find the answer: 9.0 x 10^{3} 3.0 x 10^{2}
Correct Answer
C. 3.0 x 10^1
Explanation
Dividing scientific notation: SUBTRACT the exponenent in the numerator from the exponent in the demoninator:
9.0 x 10^3 divided by 3.0 x 10^2 =
(9 divided by 3)x 10^(3-2)
11.
(8.0 x 10^{-2}) = (2 x 10^{-3})
Correct Answer
B. 4 x 10^1 = 40
Explanation
Division: Subtract the exponents: (-2) - (-3) = +1
12.
Do NOT use your calculator. UNDERSTAND how to work with scientific notation!
(10^{12 }is the same as 10^12)
(3.0x 10^{7})^{ }(4.0 x 10^{5}) =
Correct Answer
A. 12.0 x 10^12
Explanation
When MULTIPLYING in scientific notation, ADD the exponent. Make sure you change your answer to proper scientific notation.
(3.0x 10^7) (4.0 x 10^5)= (3.0 x 4.0)x 10^(7+5) = 12.0 x 10^12 = 1.2 x 10^12
13.
(8.0 x 10^{-2}) x (3 x 10^{-3}) =
Correct Answer
D. 24 x 10^(-5)
Explanation
(8.0 x 10^(-2)) x (3 x 10^(-3)) = (8.0 x 3) x (10^(-2) x 10^(-3)) = 24 x 10^(-2 - 3) = 24 x 10^(-5)
So, (8.0 x 10^(-2)) x (3 x 10^(-3)) = 24 x 10^(-5)
14.
(3.0 x 10^{2}) + (4.0 x 10^{3}) =
Correct Answer
C. 4.3 x 10^3
Explanation
To add these two numbers in scientific notation, you need to have the same exponent. In this case, you can rewrite both numbers with the same exponent: (3.0 x 10^2) + (4.0 x 10^3)
Now, you can add the numbers: (3.0 x 10^2) + (4.0 x 10^3) = 0.3 x 10^3 + 4.0 x 10^3
Since both numbers have the same exponent (10^3), you can add them: 0.3 x 10^3 + 4.0 x 10^3 = (0.3 + 4.0) x 10^3 Now, calculate the sum: (0.3 + 4.0) = 4.3 So, the result in scientific notation is: 4.3 x 10^3
15.
(9.0 x 10^{3}) - (4.0 x 10^{2})
Correct Answer
E. 8.6 x 10^3
Explanation
When substrating in scientific notation, the exponents MUST be the same. EASIEST way to do the problem: Change to "regular numbers", calculate and then change your answer back to scientific notation: (9.0 x 10^3)-(4.0 x 10^2)=
9,000 - 400 = 8,600 = 8.6 x 10^3
16.
The E coli bacterium is about 5 x 10^-7 meters wide. A hair is about 1.7 x 10^-5 meters wide. Which is wider, the bacterium or the hair?
Correct Answer
B. Hair
Explanation
The hair is wider than the E coli bacterium. The hair has a width of 1.7 x 10^-5 meters, while the bacterium has a width of 5 x 10^-7 meters. Therefore, the hair is approximately 34 times wider than the bacterium.