EDEXCEL GCSE FOUNDATION MATHS - What is the Standard Form

Edexcel GCSE Foundation Maths - What is Standard Form?

Standard form is a way of writing very large or very small numbers in a concise and convenient way. It is particularly useful when dealing with scientific measurements, where numbers can be incredibly large or small.

Understanding Standard Form

A number written in standard form consists of two parts:

1. A number between 1 and 10 (including 1 but not 10)
2. Multiplied by 10 raised to a power.

General Form:

• a x 10n

Where:

• a is a number between 1 and 10
• n is an integer (positive or negative)

Examples:

Converting to Standard Form:

1. Identify the decimal point in the original number.
2. Move the decimal point to the right or left until you have a number between 1 and 10.
3. Count the number of places you moved the decimal point. This will be the power of 10.
   • If you moved the decimal point to the left, the power will be positive.
   • If you moved the decimal point to the right, the power will be negative.

Examples:

• 3000: Move the decimal point three places to the left (3000. -> 3.000). The power is positive 3. Therefore, 3000 in standard form is 3 x 103.
• 0.005: Move the decimal point three places to the right (0.005 -> 5.000). The power is negative 3. Therefore, 0.005 in standard form is 5 x 10-3.

Converting from Standard Form:

1. Multiply the number by the power of 10.
2. Move the decimal point the number of places indicated by the power of 10.
   • If the power is positive, move the decimal point to the right.
   • If the power is negative, move the decimal point to the left.

Examples:

• 3 x 103: 3 x 103 = 3 x 1000 = 3000.
• 5 x 10-3: 5 x 10-3 = 5 x 0.001 = 0.005.

Key Points:

• Standard form provides a concise way to write very large or very small numbers.
• The number before the power of 10 must be between 1 and 10.
• The power of 10 represents the magnitude of the number.

Practice:

• Convert the following numbers to standard form:
  • 7,500,000
  • 0.00004
• Convert the following numbers from standard form:
  • 2.1 x 105
  • 6.8 x 10-4

Practice converting numbers to and from standard form will help you understand this important concept in GCSE Maths.