Standard Form

• Standard form is a way of making it easier to write very big and very small numbers. n (the power of 10) tells us the number of places to move the decimal point.
• Example 1

  • To find the number that 3.7 x103 represents, we move the decimal point 3 spaces to the right: 3.7.... 37... 370 ... 3700.
  • E.g. 3.7 x103 represents 3700.
• Example 2

  • To find the number that 5.3 x10-2 represents, we move the decimal point 2 spaces to the left: 5.3... 0.53... 0.053.
  • E.g. 5.3 x10-2 represents 0.053.
• Adding and subtracting

  • To add or subtract numbers in standard form:
  • Write the numbers in non-standard form.
  • Add or subtract.
  • Change back to standard form.
  • E.g. (5.3 x106) + (5.3 x106) = 5,300,000 + 5,300,000 = 10,600,000= 1.06 x107
• Multiplying

  • To multiply numbers in standard form:
  • Multiply the leading numbers.
  • Add the powers.
  • Change into the correct format.
  • E.g. (3 x106) x (3 x104) = 9 x1010
• Dividing

  • To divide numbers in standard form:
  • Divide the leading numbers.
  • Subtract the powers.
  • Change into the correct format.
  • E.g. (6 x107) ÷ (2 x103) = 3 x104
• The number undergoing standard form notation must have a single digit before the decimal point. 11 x 10$^3$ is not the correct standard for notation. 1.1 x 10$^4$ would be correct