Standard form is a method used to express very large and very small numbers in a way that is easier to comprehend and work with. It is also known as standard index form or scientific notation. Any number in standard form is written as: A x 10^n, where A is a number that is equal to or greater than 1 and less than 10, and n is the integer power of 10 to multiply by to get the original value.
Basics of Standard Form
The integer power of ten is positive for numbers greater than 10 and negative for values less than 1. For numbers between 1 and 10, the integer power of ten is zero. It is important to have a good understanding of place value in addition to multiplying and dividing by powers of ten.
Writing Numbers in Standard Form
To write numbers in standard form, the number must be expressed as a value between 1 and 10. The first non-zero digit is placed in the units column, followed by the decimal point and the remaining digits. Zeros at the end of the number are not necessary for a single-digit value. The number is then multiplied by 10 to the power of the number of places the decimal point moved.
Examples of Writing Numbers in Standard Form
- 800,000 in standard form = 8 x 10^5 (5 zeros make the power 5, which is positive)
- 3.9 in standard form = 3.9 x 10^0 (no zeros to determine the power, which is positive)
- 0.007601 in standard form = 7.601 x 10^-3 (3 zeros before the numbers, making the power negative)
Understanding Powers of Ten
When converting a standard form number (A x 10^n) to an ordinary (decimal) number, the value of A is multiplied by the power of 10. If n is positive, the number is larger than A, and each digit in A moves to the left. If n is negative, the number is smaller than A, and each digit in A moves to the right. If n is zero, the ordinary number is equivalent to the value of A.
Power of 10 Examples
- 10^2 = 10 x 10 = 100 (10 squared)
- 10^3 = 10 x 10 x 10 = 1000 (10 cubed)
- 10^0 = 1 (or 0.1)
- 10^-2 = 0.01
More Examples of Powers of Ten
- 9.72 x 10^4 (ordinary decimal number) = 9.72 x 10 x 10 x 10 x 10 = 9.72 x 10,000 = 9.72 x 10^4 = 97,200
- 8.1 x 10^-2 (ordinary decimal number) = 8.1 x 0.01 = 0.081 = 8.1 x 10^-2 = 0.08
Now that you have learned the basics and examples of standard form and powers of ten, you can better understand how to convert between standard form and ordinary decimal numbers, and vice versa. Keep practicing with standard form basics worksheets and writing numbers in standard form to reinforce your understanding.
