Operations-With-Standard-Form Aqa Higher

Operations with standard form

How do I perform calculations in standard form using a calculator?

• Make use of brackets around each number, and use the  button to enter numbers in standard form

  • e.g.  

  • You can instead use the standard multiplication and index buttons

• If your calculator answer is not in standard form, but the question requires it:

  • Either rewrite it using the standard process

    • e.g. 3 820 000 = 3.82 × 10⁶

  • Or rewrite numbers in standard form, then apply the laws of indices

    • e.g. 243 × 10²⁰ = (2.43 × 10²) × 10²⁰ = 2.43 × 10²²

How do I perform calculations with numbers in standard form without a calculator?

Multiplication and division

• Consider the “number parts” separately to the powers of 10

  • E.g.

    • Can be written as <img alt=”open parentheses 3 cross times 4 close parentheses cross times open parentheses 10 squared cross times 10 to the power of 5 close parentheses” data-mathml=”<math ><semantics><mrow><mfenced><mrow><mn>3</mn><mo>&#215;</mo><mn>4</mn></mrow></mfenced><mo>&#215;</mo><mfenced><mrow><msup><mn>10</mn><mn>2</mn></msup><mo>&#215;</mo><msup><mn>10</mn><mn>5</mn></msup></mrow></mfenced></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true,”toolbar”:”<toolbar ref=’general’><tab ref=’general’><removeItem ref=’setColor’/><removeItem ref=’bold’/><removeItem ref=’italic’/><removeItem ref=’autoItalic’/><removeItem ref=’setUnicode’/><removeItem ref=’mtext’ /><removeItem ref=’rtl’/><removeItem ref=’forceLigature’/><removeItem ref=’setFontFamil