Standard form

Standard Form

• Standard form or scientific notation is a way of expressing very large or very small numbers that might be cumbersome to use otherwise. This system is particularly useful in physics and engineering.
• A number in standard form is written as A × 10^n, where 1 ≤ A < 10 and n is an integer.

Writing in Standard Form

• To write a number in standard form, first rewrite the number as a decimal between 1 and 10.
• Then, consider how many places you moved the decimal point and in which direction. This will be your value of n.
• If you moved the decimal to the left to get A, then n will be positive. If you moved it to the right, n will be negative.
• For instance, 300 would be written as 3 × 10^2 and 0.003 would be written as 3 × 10^-3.

Reading Numbers in Standard Form

• Reading numbers in standard form simply requires understanding the notation A × 10^n.
• The value of n tells you how many places to move the decimal point in A. A positive n moves the point to the right, and a negative n moves it to the left.
• Learning to read numbers in standard form is important, as this notation is used widely in scientific, engineering, and mathematical contexts.

Calculating with Standard Form

• When multiplying or dividing numbers in standard form, deal with A values first and then consider powers of 10 separately.
• When adding or subtracting numbers in standard form, it’s simpler if they’ve the same power of 10. If they don’t, rearrange one or both numbers to match power.
• For example, to add 2 × 10^3 and 3 × 10^2, it’s simpler to rewrite the second term as 0.3 × 10^3 before performing the addition.
• For multiplication, multiply A’s values and add n’s values: (A1 × A2) × 10^(n1+n2).
• For division, divide A’s and subtract n’s: (A1 / A2) × 10^(n1-n2).

Standard form in Real World

• Standard form comes into its own in a real-world setting when tackling very large or small numbers, such as distances between stars in space science, or size of a bacteria in microbiology.
• In these contexts, standard form makes it easier to understand, communicate and perform calculations with such numbers. So recognising this application of standard form makes it a valuable mathematical tool.

Common Mistakes with Standard Form

• Beware of some common mistakes with standard form. Remember, A should be a number between 1 and 10, so 10 × 10^3 would not be correct.
• Be sure to also keep track of whether n should be positive or negative, depending on whether a number is larger or smaller than 1.
• Practice is key to understanding and correctly using standard form, so the more you use it, the better you’ll become.