Standard form

Standard Form

Definition and Notation

  • Standard form, also known as scientific notation, is a method of writing extremely large or small numbers.

  • A number is said to be in standard form if it is written as a x 10^n where **1 ≤ a < 10** and n is an integer.

  • For example, the number 5,000 can be written in standard form as 5 x 10^3.

  • Negative numbers can also be written in standard form. For instance, -200 would be -2 x 10^2.

Writing Numbers in Standard Form

  • A number in standard form is written with only one digit before the decimal point.

  • To transform a number into standard form, identify the decimal point and move it to the right place while adjusting the power of 10 accordingly.

  • For example, to write 340 in standard form, move the decimal point two places to the left to obtain 3.4, then multiply this by 10 raised to the number of places moved (in this case, 2) to obtain 3.4 x 10^2.

Reading numbers in Standard Form

  • When reading numbers written in standard form, remember that the exponent of 10 tells you how many places to move the decimal point.

  • If the power of 10 is positive, move the decimal point to the right. If it’s negative, move the decimal point to the left.

  • For example, the number 3.4 x 10^2 in standard form equates to 340 in standard notation

Uses of Standard Form

  • The standard form is frequently used in science, engineering, and mathematics to express very large or very small numbers, such as the distance between stars in astronomy or the size of atoms in chemistry.

  • Standard form provides an easier and simpler way of handling, comparing, and carrying out arithmetic operations on greatly disparate numbers.

Practice With Standard Form

  • Practicing converting standard notation to standard form and vice versa is key to becoming proficient in this area.

  • Practice summing, subtracting, multiplying, and dividing numbers in standard form.

  • Ensure you have a good grasp of the powers of 10 as this will make working with standard form much easier.

  • Continue to test your skills by solving real-world problems which require the use of standard form. Always revisit problem types you found challenging.