convert a number to scientific notation Quiz

1) What is the scientific form for this? 9.4*10^8

940,000,000

94,000,000,000

9.4,000,000

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.

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.

2) Write the number 4,500,000 in scientific notation.

4.5 x 10^6

45 x 10^5

4.5 x 10^-6

45,000

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.

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.

3) What is the standard form for this? 3,500,000,000

3.5*10^9

3*10^9

3.5*10^8

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.

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.

4) What is the standard form for this? 3,500,000,000

3.5*10^9

3*10^9

3.5*10^8

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.

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.

5) What is the scientific form for this? 9.4*10^8

940,000,000

94,000,000,000

9.4,000,000

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.

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.

6) Write the number 4,500,000 in scientific notation.

4.5 x 10^6

45 x 10^5

4.5 x 10^-6

45,000

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.

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.

7) Is the following numbers in proper scientific notation? 23.2 x 10²

Yes, this is proper scientific notation

No, this is not proper scientific notation

2.32 x 10^3

Explanation

2.32 x 10^3

8) Check any of the following that are correctly in scientific notation:

93 x 10^2

0.93 x 10^2

9.3 x 10^2

4 x 10^13

9.4 x 10^-12

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.

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.

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9) 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?

Bacterium

Hair

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.

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.

10) Check any of the following that are correctly in scientific notation:

93 x 10^2

0.93 x 10^2

9.3 x 10^2

4 x 10^13

9.4 x 10^-12

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.

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.

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11) Do NOT use your calculator. UNDERSTAND how to work with scientific notation! (10¹²is the same as 10^12) (3.0x 10⁷)(4.0 x 10⁵) =

12.0 x 10^12

12.0 x 10^35

1.2 x 10^13

1.2 x 10^36

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

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

12) Find the answer: 9.0 x 10³
3.0 x 10²

3.0 x 10^5

3.0 x 10^6

3.0 x 10^1

3

3.0 x 10^-1

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)

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)

13) (9.0 x 10³) - (4.0 x 10²)

5.0 x 10^1

13.0 x 10^5

9.4 x 10^3

5.0 x 10^5

8.6 x 10^3

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

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

14) (8.0 x 10^-2) x (3 x 10^-3) =

2.4 x 10^-5

24.0 x 10^-5

24.0 x 10^-6

24 x 10^(-5)

(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)

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)

15) (3.0 x 10²) + (4.0 x 10³) =

4.3 x 10^2

7.0 x 10^-1

4.3 x 10^3

7.0 x 10^5

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

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