Scientific Notation ( Free Worksheets, Solved Examples and More)

Scientific notation is a standard form of writing very small and very big numbers so that they can easily be used for computations and other calculations. A number in scientific notation is of the form a × 10ⁿ, where a is a number between 1 and 9, inclusive and n can be a positive or a negative integer.

For example: 300 is written as 3 × 10² in scientific notation.Let us now learn more about scientific notation and the steps for adding, subtracting, multiplying, and dividing scientific notation.

Do you already know how to solve scientific notations? Get straight to the free scientific notation worksheets!

Scientific Notation Worksheets – Addition, Subtraction, Division and Multiplication

Before we move on to the scientific notation worksheets, let us understand the concept a bit more. In a scientific notation, the decimal point of a number is moved till we get a number from 1 to 9 and value of n is the number of places the decimal is moved.

The exponent will be positive if we move the decimal point toward the left. If we move the decimal point towards the right, the exponent will be negative.

See the examples below:

Example: Write 8,380,000 in scientific notation.

8,380,000 is a whole number so decimal point will be at the end of the number, so here a = 8.38

Now n is the number of places the decimal is moved. Here we moved the decimal point towards the left, so exponent will be positive. So, n = 6.

So, 8,380,000 in scientific notation is written as 8.38 × 10⁶

Example: Write 0.00061 in scientific notation.

Here we move the decimal to the right so that we get a number from 1 to 9. So, a = 6.1

n is the number of places the decimal is moved. Here we moved the decimal point towards the right, so exponent will be negative. So, n = -4.

So, 0.00061 in scientific notation is written as 6.1 × 10^-4

Adding and Subtracting Scientific Notation Worksheets with Solved Examples

We know how to write numbers in scientific notation, which means numbers have the same base that is 10. Next, let us go through the steps to be followed for adding or subtracting:

Step 1: Make the exponents equal to each other for which we should make the smaller exponent equal to the larger one by dividing with appropriate power of 10.

Step 2: Add or subtract the new coefficients.

Step 3: Write the answer in scientific notation, if it is not in scientific notation after adding or subtracting.

Example: Subtract 5.66 × 10¹ – 3 × 10^-2

Here -2 is the smaller exponent, so multiply 3 × 10^-2 by 10³ to make it 10¹and divide by 10³,

So, 3 × 10^-2 = $\frac{3\times10^{-2}\times10^3}{10^3}$ = $\frac{3\times10^{-2+3}}{10^3}$ = $\frac{3\times10^1}{10^3}$ = $\frac{3}{10^3}\times10^1$ = $0.003\times10^1$

Now 5.66 × 10¹ – 3 × 10^-2 = 5.66 × 10¹ – 0.003 × 10¹ = (5.66 – 0.003) × 10¹ = 5.657 × 10¹

Multiplying and Dividing Scientific Notation Worksheets and Solved Examples

To multiply or divide the numbers in scientific notation, we multiply or divide their coefficients and add their exponents. If after adding or subtracting the coefficients, the answer is not in scientific notation, then convert it to scientific notation.

Step 1: Multiply or divide the coefficients.

Step 2: Add or subtract the exponents.

Step 3: Convert the answer in scientific notation.

Example: Multiply (3.1 × 10^-1)(0.4 × 10²)

Step 1: Multiply 3.1 and 0.4 that is 3.1 × 0.4 = 1.24

Step 2: Add the exponents, 10^-1 × 10² = 10^-1+2 = 10¹

Step 3: (3.1 × 10^-1)(0.4 × 10²) = 1.24 × 10¹

CHECK POINT

Simplify and write each of the following in scientific notation.

0.000251
0.792 × 10⁵
(6.3 × 10^-2)(6.2 × 10²)
(5.4 × 10^-1) ÷ (2.7 × 10¹)
(3 × 10^-2)(9 × 10⁴)
(3.6 × 10³) ÷ (0.6 × 10³)

Answer key

2.51 × 10^-4
7.92 × 10⁴
3.906 × 10¹
2 × 10^-2
2.7 × 10³
6

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FAQs

What is a scientific notation?

Scientific notation is a method used to represent very large or very small numbers in a more compact and readable form. It is written in the form of a number between 1 and 10 multiplied by a power of 10.

How to convert a number to scientific notation?

To convert a number to scientific notation, move the decimal point to the left or right so that there is one non-zero digit to the left of the decimal point. Count the number of places you moved the decimal point and add that as an exponent to 10.

How do you add and subtract numbers in scientific notation?

To add or subtract numbers in scientific notation, the exponents must be the same. If they are not, one number must be converted so that the exponents are the same. Once the exponents are the same, the numbers can be added or subtracted.

How do you multiply and divide numbers in scientific notation?

To multiply numbers in scientific notation, multiply the numbers and add the exponents. To divide numbers in scientific notation, divide the numbers and subtract the exponents.

What are some common uses of scientific notation?

Scientific notation is commonly used in scientific fields such as astronomy, physics, and chemistry to represent very large or very small numbers. It is also used in engineering and finance.

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