How To Convert Scientific Notation To Standard Form

Key Concept’s on How to Convert Scientific Notation To Standard Form 

It is essential for students to understand the logic behind converting scientific notation to standard form by doing an exploratory activity instead of memorizing the rules of shifting the decimal. An exploratory activity helps students understand why it makes sense to shift the decimal according to the power of 10. In this blog, we talk about how you can teach students about converting scientific notation to standard form.

Different forms of numbers in converting scientific notation:

There are two different types of scientific notation problems. One form has a positive exponent, and the other form has a negative exponent. Here are some examples:

How do you teach students to convert scientific notation to standard form?

Step 1: Expand the exponents

Have students complete the following table independently.

When it looks like students are done, ask a student or multiple students to fill in the table on the board. 

Step 2: Identify the direction to shift the decimal point.

Have students complete the following table independently.

Positive exponent: 2.1×10⁵ is bigger than 2.1. So, the decimal must be moved to the right.

Negative exponent: 3.7×10⁻⁵ is smaller than 2.1. So, the decimal must be moved to the left.

Step 3: Write standard form.

Once students have decided on the direction for the decimal shifting, then ask the student to find the absolute value of the exponent because it represents the number of places the decimal needs to be shifted.

Step 4: Discussion

• Allow students to talk or work together.
  • Hints you can give throughout:
    • Tell them to focus on the sign of the exponent in the scientific notation and its absolute value. How do those values are helpful to find a standard form?
• For positive exponents: Suppose the scientific notation is ax10^b , then move the decimal point b places to the right of a to find the standard form.
• For negative exponents: Suppose the scientific notation is ax10^-b , then move the decimal point b places to the left of a to find the standard form.

Examples

Example 1: Converting scientific notation with a positive exponent to standard

Step 1:

Step 2:

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The number is bigger than its coefficient, therefore the decimal will shift 5 places to the right.

Example 2: Converting scientific notation with a negative exponent to standard

Why teach converting scientific notation to standard form this way?

Teaching converting scientific notation to standard form this way allows students to discover the reasoning behind the shifting of decimals. This creates a deeper conceptual understanding.

Vocabulary for teaching converting scientific notation to standard form

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

• A negative exponent does not mean the value is negative!
  • Consistently remind students that negative exponents make the value small, not negative!
• Students may shift the decimal in the right direction for a negative exponent.
  • Remind students that negative exponents make the value small, so shift the decimal point to the left.

Resources

• Downloadable worksheet for practicing converting scientific notation to standard form
• Quiz for assessing converting scientific notation to standard form

Frequently asked questions about converting scientific notation to standard form