standard form

• Standard form is a way of writing big and small numbers quickly and efficiently
• Number in standard form

  Some number between 1 and 10 multiplied by a power of 10
• The number between 1 and 10 must be a whole number
• If the power of 10 is positive, the number is a big number
• If the power of 10 is negative, the number is a small number
• Writing a big number in standard form

  • 6 x 10^9
  • 6.3 x 10^9
  • 5.02 x 10^6
• Writing a small number in standard form

  • 6 x 10^-7
  • 6.3 x 10^-7
  • 3.05 x 10^-3
• Converting standard form to ordinary number

  1. Write the first digit

  2. Count the number of digits after the first digit

  3. Write the number with commas every 3 digits
• Calculating with standard form

  1. Deal with the numbers separately

  2. Multiply/divide the numbers

  3. Add/subtract the powers of 10
• If the result is not between 1 and 10, adjust by dividing/multiplying by 10 and adjusting the power of 10
• Using a calculator with standard form

  1. Type the number in standard form using the calculator's standard form button

  2. Perform the calculation
• The final answer should be given to the appropriate number of significant figures
• Calculating with standard form

  1. Type number in calculator

  2. Press standard form button

  3. Enter exponent

  4. Perform calculation

  5. Square root result to get final answer

  6. Round to 2 significant figures

  7. Express in standard form
• Anything to the power of 0 is 1
• When dividing, subtract the exponents
• When multiplying, add the exponents
• Numbers in standard form must be between 1 and 10
• To convert a number to standard form, move the decimal point to get a number between 1 and 10, then adjust the exponent accordingly
• Calculating P squared

  1. Substitute X and Y values

  2. Perform calculation on calculator

  3. Square root result to get P

  4. Round P to 2 significant figures

  5. Express P in standard form
• The answer for P is 4.9 x 10^-5