Scientific Notation -standard Form

1) The Earth's circumference is approximately ____________________. In scientific notation, this is 4 X 10⁷ m.

The Earth's circumference is approximately 40,000,000 meters. This can also be expressed as 4 X 10^7 meters in scientific notation.

Explanation

The Earth's circumference is approximately 40,000,000 meters. This can also be expressed as 4 X 10^7 meters in scientific notation.

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2) Match Scientific Notation with Standard Form. Use examples to identify the correct matching form. Demonstrate understanding of scientific notation by forming an equivalent rational number represented in standard form.

6.06 X 10^3

9.4 X 10 ^7

8.3 X 10 ^6

1.234 X 10^4

Scientific Notation: to Standard Form/ Decimal Notation:
move the decimal separator point the required amount n spaces, to make the number's value within a desired range, between 1 and 10 for standard notation.
If the decimal was moved to the left, a x 10n ;
to the right, x 10-n.

Explanation

Scientific Notation: to Standard Form/ Decimal Notation:
move the decimal separator point the required amount n spaces, to make the number's value within a desired range, between 1 and 10 for standard notation.
If the decimal was moved to the left, a x 10n ;
to the right, x 10-n.

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3) Is this statement true or false? The Earth's mass is about 5,973,600,000,000,000,000,000,000 kg. In scientific notation, this is written as 5.9736 X 10²⁴ kg.

True

False

The statement is true because the Earth's mass is indeed approximately 5,973,600,000,000,000,000,000,000 kg, which can be expressed in scientific notation as 5.9736 x 10^24 kg.

Explanation

The statement is true because the Earth's mass is indeed approximately 5,973,600,000,000,000,000,000,000 kg, which can be expressed in scientific notation as 5.9736 x 10^24 kg.

4) Match the following: Match Scientific Notation with Standard Form. Use example to help identify the correct matching form. Demonstrate understanding of scientific notation by forming an equivalent rational number represented in standard form.

7.89 X 10 ^ -5

5.75 × 10^-3

2.75 × 10^-4

7.8×10 ^ -7

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5)

8003

8030

0.803

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6) Find the answer to the following question in Scientific Notation: 0.0000056 =

56 X 10 ^-6

5.6 X 10 ^6

5.6 X 10 ^-6

5.6 X 10 ^-5

The given number is 0.0000056, which can be written in scientific notation as 5.6 x 10^-6. This is because the decimal point is moved 6 places to the right, resulting in a coefficient of 5.6, and the exponent is negative since the original number is less than 1.

Explanation

The given number is 0.0000056, which can be written in scientific notation as 5.6 x 10^-6. This is because the decimal point is moved 6 places to the right, resulting in a coefficient of 5.6, and the exponent is negative since the original number is less than 1.

7) Which of the following numbers is correctly expressed in scientific notation?

0.52 x 104

12.7 x 10-2

3.06 x 105

0.0084 x 103

Scientific notation expresses numbers as a coefficient between 1 and 10 multiplied by a power of 10. This simplifies very large or small numbers. For example, 3,000,000 can be written as 3 x 106. The coefficient is 3, and the power of 10 indicates how many places the decimal moves. A positive exponent (like 6) means a large number; a negative exponent would indicate a very small number.

Explanation

Scientific notation expresses numbers as a coefficient between 1 and 10 multiplied by a power of 10. This simplifies very large or small numbers. For example, 3,000,000 can be written as 3 x 106. The coefficient is 3, and the power of 10 indicates how many places the decimal moves. A positive exponent (like 6) means a large number; a negative exponent would indicate a very small number.

8) SELECT ALL OF THE CHOICES IN SCIENTIFIC NOTATION BY CHECKING BELOW

536,000

5.36 X 10 ^ 5

0.356

7.8 X 10 ^ -3

3.56 X 10 ^2

450

5.67 X 10 ^ -5

0.700 X 10^5

927.00

The correct answer choices are all written in scientific notation, which is a way to express very large or very small numbers using powers of 10. In scientific notation, a number is written as a coefficient multiplied by 10 raised to a power. For example, 5.36 x 10^5 means 5.36 multiplied by 10 raised to the power of 5. The other answer choices that are also in scientific notation follow the same pattern, with a coefficient and a power of 10.

Explanation

The correct answer choices are all written in scientific notation, which is a way to express very large or very small numbers using powers of 10. In scientific notation, a number is written as a coefficient multiplied by 10 raised to a power. For example, 5.36 x 10^5 means 5.36 multiplied by 10 raised to the power of 5. The other answer choices that are also in scientific notation follow the same pattern, with a coefficient and a power of 10.

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