How to Convert Numbers From and To Scientific Notation: 14 Steps

2024 Author: Jason Gerald | [email protected]. Last modified: 2024-01-15 08:07

Scientific notation is commonly used in chemistry and physics to represent very large or very small numbers. Converting numbers from and into scientific notation is not as difficult as it seems. Just follow these steps to find out how to do it.

Step

Method 1 of 2: Converting Numbers Into Scientific Notation

Step 1. Start with very small or very large numbers

You have to start with very small or very large numbers if you want to successfully convert them to scientific notation. For example, 10,090, 250,000,000 is a very large number; 0.0004205 is a very small number.

Step 2. Cross out the decimal point of the starting number

This is the first step to converting numbers into scientific notation. If you're using the number 0.00004205, just write x above the decimal point.

Step 3. Add a new decimal point to the number so that there is only one nonzero digit in front of it

In this case, the first nonzero number is 4, so put a decimal point after 4 so the new number becomes 000004, 205.

This also applies to large numbers. For example, 10,090,250,000,000 becomes 1.0090250000000

Step 4. Rewrite this number to remove unnecessary digits

Unnecessary digits are zeros that are not among non-zero numbers.

• For example, in the number 1.0090250000000, trailing zeros are not required, but zeros between 1 and 9, and between 9 and 2, are required. Rewrite this number as 1.009025.
• In 000004, 205, leading zeros are not required. Rewrite this number as 4, 205.

Step 5. Write x 10 after the new number

For now, just write 4, 205 x 10.

Step 6. Count the number of times you moved your starting decimal point

In the problem 0.00004205 becomes 4, 205, you move the decimal point 5 times. In the problem 10,090,250,000,000 becomes 1.0090250000000, you move the decimal point 13 times.

Step 7. Write the number as a power over the number 10

For 1.0090250000000, write x 10¹³. For 4, 25, write x 10⁵.

Step 8. Determine if the exponent is negative or positive

If your starting number is very large, the exponent must be positive. If your starting number is very small, the exponent must be negative.

For example: the very large number 10,090,250,000,000 becomes 1.009025 x 10 ¹³ while the very small number 0.0004205 becomes 4.205 x 10^-5.

Step 9. Round up your number as needed

This depends on the accuracy of your answer. For example, 1.009025 x 10¹³ maybe it's better to write 1,009 x 10¹³ or even just 1.01 x 10¹³, depending on the level of accuracy you need.

Method 2 of 2: Converting Numbers From Scientific Notation

Step 1. Decide if you want to move the decimal point left or right

If the exponent in x 10 is positive, then you move the decimal point to the right; if the exponent is negative, you move the decimal point to the left.

Step 2. Write down the number of times you have to move the decimal point

In problem 5, 2081 x 10¹², you will move the decimal point five steps to the right. If the power is -7, you move left by 7 steps; if the power is 5, move it five steps to the left.

Step 3. Move the decimal point, adding zeros to the blanks

You may have to add it before or after the number, depending on where you move the decimal point, left or right. If you move the decimal point 12 steps to the right from 5, 2081, the new number becomes 5208100000000.

Step 4. Write down the new decimal point after you've moved it the correct number of steps

Step 5. Add dots to any number greater than 999

Trace the digits, from right to left, placing a dot in front of each group of three digits. For example, 5208100000000 becomes 5,208,100,000,000.