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