How To Convert Standard Form To Scientific Notation

Key Concepts of Standard Form To Scientific Notation

It is essential for students to understand the logic behind converting standard form to scientific notation by doing an exploratory activity instead of memorizing the rules of shifting the decimal. An exploratory activity helps students to identify the coefficient and exponent for the scientific notation from the standard form. In this blog, we talk about how you can teach students about converting standard form to scientific notation.

Different forms of converting standard form to scientific notations:

There are two types of numbers in standard form. One form has a very large number and another form has a very small number. Here are some examples:

• Very large numbers
  • 23400000 = ?
  • 5000000 = ?
• Very small numbers
  • 0.0000003 = ?
  • 0.000000234 = ?

How do you teach converting standard form to scientific notation?

First, talk about the coefficients of scientific notation and how to identify them.

Decimal shifting is a great way to teach students how to identify the coefficient and power of 10 of a scientific notation from standard form. 

Step 1: Identify the coefficient of scientific notation

Remind students that the coefficient of scientific notation is a number between 1 and 10. If there is no decimal in the given number, then we have to assume that there is a decimal point at the end of the number.

Example 1: When the Standard form is 64,000,000.

The coefficient of 64,000,000 is 6.4.

Example 2: When the Standard form is 0.00023.

The coefficient of 0.00023 is 2.3.

Step 2: Predict the exponent

Ask the student to count how many times we moved the decimal to make the coefficient and tell them to focus on the direction in which the decimal shifts. If the decimal shifts from left to right then the exponent must be negative and if the decimal shifts from right to left then the exponent must be positive.

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Example 1: When the Standard form is 64,000,000.

Decimal shifts 7 places to the left. Therefore the exponent must be 7.

Example 2: When the Standard form is 0.00023.

Decimal shifts 4 places to the right. Therefore the exponent must be -4.

Step 3: Write the scientific notation

Remind students of scientific notation.

Example 1: When the Standard form is 64,000,000.

Coefficient: 6.4

Exponent: 7

Scientific notation of 64,000,000 is 6.4×10⁻⁷.

Example 2: When the Standard form is 0.00023.

Coefficient: 2.3

Exponent: -4

Scientific notation of 0.00023 is 2.3×10⁻⁴.

Examples

Example 1: Converting very large numbers to scientific notation

Step 1:

The coefficient of 37,000,000,000 is 3.7.

Step 2:

Decimal shifts 10 places to the left. Therefore the exponent must be 10.

Step 3:

Coefficient: 3.7

Exponent: 10

Scientific notation of 37,000,000,000 is 3.7×10^10.

Example 2: Converting very small numbers to scientific notation

Step 1:

The coefficient of 0.0000058 is 5.8.

Step 2:

Decimal shifts 6 places to the right. Therefore the exponent must be -6.

Step 3:

Coefficient: 5.8

Exponent: -6

Scientific notation of 0.0000058 is 5.8 x 10⁻⁶.

Why teach converting standard form to scientific notation this way?

Using a visual representation of decimal shifting students can easily identify the coefficient which is a number between 1 to 10. It can also help the students to find the number of places the decimal has moved and its directions. After identifying the coefficient and exponent, students can easily write the scientific notation.

Also read: How To Find The GCF – Teaching GCF With Examples

Vocabulary for teaching converting standard form to scientific notation

Exponent: An exponent (or power) is a small number placed to the upper-right of a base. It shows how many times the base is multiplied by itself.

Coefficient: The number in front of the multiplication sign in a number written in scientific notation, it will be greater than or equal to 1 and less than 10 (1 ≤ N < 10).

Scientific notation: A way of writing very large or very small numbers using a number between 1 and 10 multiplied by a power of ten.

Standard form: The usual way that numbers are written, with digits and a decimal point.

Misconceptions and errors students are likely to have

• Students may write all non-zero digits as the coefficient.
  • Consistently remind students that a coefficient is a number between 1 and 10
• Students may write the opposite sign for the exponent.
  • Remind students that if the decimal shifts from left to right then the exponent must be negative and if the decimal shifts from right to left then the exponent must be positive.

Resource:

Downloadable worksheet for practicing converting standard form to scientific notation

Frequently Asked Questions On How To Convert Standard Form To Scientific Notation?