Scientific Notation: Writing Numbers in Scientific Notation and Standard Form, Exams of Science education

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Scientific Notation

Section 7-1 Part 2

Goals

Goal

• To write numbers in scientific notation and standard form.
• To compare and order numbers using scientific notation.

The table shows relationships between several powers of 10.

• Each time you divide by 10, the exponent in the power decreases by 1 and the decimal point in the value moves one place to the left.
• Each time you multiply by 10, the exponent in the power increases by 1 and the decimal point in the value moves one place to the right.

Powers of 10

Powers of 10

• You can find the product of a number and a power

of 10 by moving the decimal point of the number.

• If the exponent is positive, move the decimal point to the right.
• If the exponent is negative, move the decimal point to the left.
• You may need to write zeros to the right or left of

the number in order to move the decimal point.

A. 2.5 x 10 5

Multiply.

2.5 0 0 0 0 Since the exponent is a positive 5, move the decimal point 5 places to the right. 250, B. 10.2 x 10

• 3 0 10. Since the exponent is a negative 3, move the decimal point 3 places to the left.

Your Turn:

Definition

• Scientific Notation - is a way to express numbers

that are very large or very small.

• Powers of 10 are used when writing numbers in scientific notation.
• Numbers written in scientific notation are expressed as 2 factors. - One factor is a number greater than or equal to 1. - The other factor is a power of 10.
• Example:
  • 1.43 ⨯ 10 12

  • 5.8 ⨯ 10

Why Use Scientific Notation?

• For very large and very small numbers, these numbers can be converted into scientific notation to express them in a more concise form.
• Numbers expressed in scientific notation can be used in a computation with far greater ease.

Example: Recognizing Scientific Notation Is the number written in scientific notation? Explain.

4

2

No, 53 is not less than 10 Yes No, 0.35 is not greater than or equal to 1 No, 100 is not in power of 10 form

Procedure: Writing Numbers in Scientific Notation

1. Place the decimal point so that there is one non-

zero digit to the left of the decimal point.

2. Count the number of decimal places the decimal

point has “moved” from the original number.

This will be the exponent on the 10.

3. If the original number was less than 1, then the

exponent is negative. If the original number was

greater than 1, then the exponent is positive.

Think: The number is less than 1, so the exponent will be negative. A. 0.00709 Think: The decimal needs to move 3 places to get a number between 1 and 10. 7.09 x 10

• 3 Write the number in scientific notation. So 0.00709 written in scientific notation is 7.09 x 10

Example: Writing Numbers in Scientific Notation

Think: The number is less than 1, so the exponent will be negative.

A. 0.

Think: The decimal needs to move 4 places to get a number between 1 and 10.

8.11 x 10

Write the number in scientific notation.

So 0.000811 written in scientific notation is 8.11 x 10

• .

Your Turn:

Think: The number is greater than 1, so the exponent will be positive. B. 480,000, Think: The decimal needs to move 8 places to get a number between 1 and 10. 4.8 x 10 8 Write the number in scientific notation. So 480,000,000 written in scientific notation is 4.8 x 10 8

Your Turn:

Procedure: Writing Numbers in Standard Form

1. Simply move the decimal point to the right for positive exponent 10.
2. Move the decimal point to the left for negative exponent 10. (Use zeros to fill in places.)

135, Think: Move the decimal right 5 places. A. 1.35 x 10 5 1.35 x 10 5 Write the number in standard form. Example: Writing a Number in Standard Form