2. Which number represents 4.6 x 10^-4 in standard form?
A. 0.00046
B. 460,000
C. 0.000046
D. 46,000
3. Yoshi wrote the number 7,614,000 in scientific notation. Type the number in the empty box given below to complete the scientific notation.
__ x 10^6
4. Which numbers are less than 1,000? Mark all that apply.
A. 8 x 10^2
B. 9 x 10^3
C. 5 x 10^1
D. 3 x 10^4
5. Which of the following numbers is not written in scientific notation?
A. 0.5 x 10^-12
B. 6 x 10^2
C. 7.23 x 10^-3
D. 1.7 x 10^4
6. 5 x 10^6 is how many times greater than 5 x 10^2?
5 x 10^6 is ____times greater than 5 x 10^2
7. Which of the following is NOT a true statement?
A. 8 x 10^-4 is 1,000 times as great as 9 x 10^-7
B. 4 x 10^8 is 100 times as great as 4 x 10^6
C. 2 x 10^6 is 10 times as great as 2 x 1^5
D. 7 x 10^-2 is 1,000 times as great as 7 x 10^-6
8. Choose the appropriate sign for each of the following expressions in the table. 1.98 x 10^5 ? 8.91 x 10^5, 2.14 x 10^5 ? 2.4 x 10^3, 8.341 x 10^-6 ? 2.15 x 10^-2. The options for ? are <, >, or =.
9. When doing a computer calculation, Cooper got an answer that said 1.45E - 12. What is this number in scientific notation?
A. 1.45 x 10^-12
B. 1.45 + 19^-12
C. 1.45 x 10^12
D. -12 x 10^1.45
10. The combined volume of all the tanks at an aquarium is 2.25 x 10^4 gallons. The aquarium plans to install a new dolphin tank with a volume of 350,000 gallons. What will be the total volume of all of the tanks at the aquarium after the new dolphin tank is installed?
A. 5.75 x 10^5
B. 5.75 x 10^4
C. 3.725 x 10^4
D. 3.725 x 10^5
11. Express your answer in scientific notation. 8.3 x 10^9 - 2.1 x 10^7
A. -8.279 x 10^9
B. 6.20 x 10^2
C. 8.279 x 10^9
D. -6.20 x 10^2
12. A rectangular section of wilderness will be set aside as a new wildlife refuge. Its dimensions are 6 x 10^3 meters by 3 x 10^4 meters. Find the area of the land in square meters. Put your answer in scientific notation.
A. 1.8 x 10^8
B. 9.0 x 10^9
C. 18 x 10^7
D. 90 x 10^8
13. Multiply the expression on the left and match them with their appropriate result. (2 x 10^-3) x (3 x 10^7), (9.1 x 10^9) x (2.6 x 10^2), (6.77 x 10^-12) x *1.12 x 10^-6). Options are (6 x 10^4), (2.366 x 10^-12), and (7.5824 x 10^-18).
14. Write the following quotient in scientific notation: (1.9 x 10^8) divided by (2 x 10^3)
__ x 10^4
15. What is the quotient of the following expression? (5.6 x 10^2) divided by (1.4 x 10^-6)
A. 4 x 10^8
B. 4 x 10^7
C. 4 x 10^10
D. 4 x 10^9
2. The number 4.6 x 10^-4 in standard form is A. 0.00046.
3. Yoshi wrote the number 7,614,000 in scientific notation. The number in scientific notation is 7.614 x 10^6.
4. The numbers that are less than 1,000 are A. 8 x 10^2, C. 5 x 10^1, and D. 3 x 10^4.
5. The number that is not written in scientific notation is B. 6 x 10^2.
6. 5 x 10^6 is 10,000 times greater than 5 x 10^2.
7. The statement that is NOT true is A. 8 x 10^-4 is 1,000 times as great as 9 x 10^-7.
8. The appropriate signs for the expressions are: 1.98 x 10^5 > 8.91 x 10^5, 2.14 x 10^5 > 2.4 x 10^3, and 8.341 x 10^-6 < 2.15 x 10^-2.
9. The number 1.45E - 12 in scientific notation is A. 1.45 x 10^-12.
10. The total volume of all the tanks at the aquarium after the new dolphin tank is installed will be 5.75 x 10^5 gallons.
11. The expression 8.3 x 10^9 - 2.1 x 10^7 in scientific notation is C. 8.279 x 10^9.
12. The area of the land in square meters is 1.8 x 10^8 square meters.
13. (2 x 10^-3) x (3 x 10^7) = 6 x 10^4, (9.1 x 10^9) x (2.6 x 10^2) = 2.366 x 10^-12, and (6.77 x 10^-12) x (1.12 x 10^-6) = 7.5824 x 10^-18.
14. The quotient (1.9 x 10^8) divided by (2 x 10^3) in scientific notation is 9.5 x 10^4.
15. The quotient of (5.6 x 10^2) divided by (1.4 x 10^-6) is C. 4 x 10^10.
2. To convert 4.6 x 10^-4 to standard form, we multiply the base number (4.6) by the power of 10 raised to (10^-4). This means moving the decimal point in 4.6 four places to the left. The correct answer is A. 0.00046.
3. The number 7,614,000 can be written in scientific notation as 7.614 x 10^6. We move the decimal point three places to the left and multiply by 10^6.
4. To determine which numbers are less than 1,000, we compare the exponents of 10. A number with an exponent smaller than 3 (10^3) will be less than 1,000. Based on this, the correct answer is C. 5 x 10^1.
5. A number written in scientific notation should have only one digit before the decimal point. Based on this, the number B. 6 x 10^2 is not written in scientific notation because it has two digits before the decimal point.
6. To determine how many times greater 5 x 10^6 is than 5 x 10^2, we divide the larger number by the smaller number. (5 x 10^6)/(5 x 10^2) = 10^4. So, 5 x 10^6 is 10,000 times greater than 5 x 10^2.
7. Checking each statement, we find that statement C. 2 x 10^6 is 10 times as great as 2 x 1^5 is not a true statement. The correct answer is C.
8. To compare the expressions, we compare the exponents. For the first expression, 1.98 x 10^5 > 8.91 x 10^5 because the exponent of the first number is smaller. For the second expression, 2.14 x 10^5 > 2.4 x 10^3 because the exponent of the first number is larger. For the third expression, 8.341 x 10^-6 < 2.15 x 10^-2 because the exponent of the first number is larger. The answers are >, >, and <.
9. The notation E - 12 represents 10 raised to the power of -12. So, 1.45E - 12 is equivalent to 1.45 x 10^-12. The correct answer is A.
10. To find the total volume of all the tanks, we need to add the combined volume of the pre-existing tanks (2.25 x 10^4 gallons) to the volume of the new dolphin tank (350,000 gallons). The sum is 3.725 x 10^5 gallons. The correct answer is D.
11. To subtract numbers written in scientific notation, we need to ensure that the exponents are the same. In this case, we subtract 2.1 x 10^7 from 8.3 x 10^9, keeping the exponent the same. The answer is 8.279 x 10^9. The correct answer is C.
12. To find the area of the land, we multiply the length (6 x 10^3 meters) by the width (3 x 10^4 meters). This gives us an area of 18 x 10^7 square meters. The correct answer is C.
13. Calculating each expression:
(2 x 10^-3) x (3 x 10^7) = 6 x 10^4
(9.1 x 10^9) x (2.6 x 10^2) = 2.366 x 10^12
(6.77 x 10^-12) x *1.12 x 10^-6) = 7.5824 x 10^-18
The correct option is (6 x 10^4), (2.366 x 10^-12), and (7.5824 x 10^-18).
14. To divide numbers written in scientific notation, we divide the base numbers and subtract the exponents. (1.9 x 10^8) divided by (2 x 10^3) = 0.95 x 10^5. The correct answer is 0.95 x 10^4.
15. Dividing (5.6 x 10^2) by (1.4 x 10^-6), we divide the base numbers and subtract the exponents. (5.6 / 1.4) x 10^(2-(-6)) = 4 x 10^8. The correct answer is A. 4 x 10^8.
2. C. 0.000046
3. 7.614 x 10^6
4. A. 8 x 10^2, C. 5 x 10^1
5. B. 6 x 10^2
6. 10,000 times greater
7. C. 2 x 10^6 is 10 times as great as 2 x 10^5
8. <, >
9. A. 1.45 x 10^-12
10. A. 5.75 x 10^5
11. C. 8.279 x 10^9
12. D. 90 x 10^8
13. (6 x 10^4), (7.5824 x 10^-18)
14. 9.5 x 10^4
15. C. 4 x 10^10