Table of Contents

Last modified on August 3rd, 2023

chapter outline

 

Converting Scientific Notation to Standard Form

As we know, scientific notation is the way to represent very large or very small numbers in (a × 10n) form. Here ‘a’ is the coefficient having a number greater than or equal to 1, and ‘n’ is the exponent or power with base 10. In contrast, the standard form is written as a single number with no multiplication sign or exponents.

Here are a few steps one should remember for converting a number in scientific notation to standard form.

Steps with Examples

  • Step 1: Identify the exponent (n) in the power of 10
  • Step 2: Shift the decimal that number of places to the right when the exponent is positive and to the left when the exponent is negative
  • Step 3: Fill up the empty spaces with 0

Example -1 (with Positive Exponent)

Let us see how to convert 4.7 × 103

  • Step 1: The exponent is 3
  • Step 2: Since 3 is positive, we will shift the decimal 3 places to the right
  • Step 3: After filling the empty spaces with 0, we get 4,700

Thus the standard form of 4.7 × 103 is 4,700

Example – 2 (with Negative Exponent)

Convert 1.52 × 10−2 to standard form

  • Step 1: The exponent is -2
  • Step 2: Since -2 is negative, we will shift the decimal 2 places to the left
  • Step 3: After filling the empty spaces with 0, we get 0.0152 or .0152

Thus the standard form of 1.52 × 10−2 is 0.0152

E.g. 1.

Convert 8.235 x 105 to standard form.

Solution:

As we know,
In 8.235 × 105, a = 8.235, n = 5
Since 5 is positive, we will shift the decimal 5 places to the right
After filling the empty spaces with 0, we get 823500

Write 2.57 × 10−3 in standard form.

Solution:

As we know,
In 2.57 × 10−2, a = 2.57, n = -3
Since -3 is negative, we will shift the decimal 3 places to the left
After filling the empty spaces with 0, we get 0.00257
Thus the standard form of 2.57 × 10−2 is 0.00257

Last modified on August 3rd, 2023

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