Table of Contents

Last modified on August 3rd, 2023

As we know, scientific notation is the way to represent very large or very small numbers in (a × 10^{n}) 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.

**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 × 10^{3}

**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 × 10^{3} 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 10 ^{5 }to standard form.**

Solution:

As we know,

In 8.235 × 10^{5}, 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