INDICES and STANDARD FORM

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Exercise 1. 1) Write the following numbers in standard form. a) 35, b) 4210, c) 125⋅002, d) 9⋅2, e) 125000, f) 8, g) 0⋅025, h) 0⋅00167, i) 100, j) 1, k) 251. 2) Work out the following. Give your answers in standard form. a) (3.5 × 10 7 ) + (2⋅6 × 10 5 ), b) (3⋅9 × 10 6 ) × (2.1 × 10 −3 ), c) 2 ( 3× 10 ) 3 ( 3× 10 − ) , d) (4⋅25×10 6 ) − (3⋅456×10 4 ), e) (7⋅29×10 12 ) ÷ (3⋅5×10 8 ), f) g) (3.2 × 10 4 ) × (2.5 × 10 3 ), h) 3.6 × 10 . 5 i) ( ) 3 4 ( 36× 10 ) 3 ( 8⋅ 5× 10 ) 8.6 × 6 10 4.3 × 10 − , 3 , 3) The following numbers have been written in standard form. Write each in decimal form. a) 3.5 × 10 6 , b) 8.2 × 10 −3 . 4) Find, in standard form, the values of a) (3 × 10 2 ) × (2 × 10 3 ), b) (4 × 10 2 ) × (2 × 10 4 ), c) (3 × 10 3 ) × (3 × 10 5 ), d) (3.1 × 10 7 ) × (2 × 10 3 ), e) (4.3 × 10 2 ) × (2 × 10 6 ), f) (3.2 × 10 5 ) × (3 × 10 −2 ), g) (3.3 × 10 −2 ) × (3 × 10 −1 ), h) (4.8 × 10 −3 ) × (2 × 10 −2 ), i) (1.5 × 10 −2 ) × (4 × 10 5 ). 5) Find, in standard form, the values of a) (6 × 10 2 ) × (2 × 10 3 ), b) (9 × 10 2 ) × (2 × 10 4 ), c) (6 × 10 3 ) × (3 × 10 5 ), d) (8 × 10 7 ) × (5 × 10 3 ), e) (25 × 10 2 ) × (5 × 10 6 ), f) (30 × 10 5 ) × (4 × 10 −2 ), g) (3.1 × 10 4 ) × (6 × 10 −1 ), h) (7.8 × 10 5 ) × (2 × 10 −2 ), i) (12 × 10 3 ) × (11 × 10 5 ). ©www.mathsguru.co.uk
ANSWERS / SOLUTIONS. 1) a) 3⋅5 × 10 1 , b) 4⋅21 × 10 3 , c) 1⋅25002 × 10 2 , d) 9⋅2 × 10 0 , e) 1⋅25 × 10 5 , f) 8×10 0 , g) 2⋅5 × 10 −2 , h) 1⋅67 × 10 −3 , i) 1 × 10 2 , j) 1 × 10 0 , k) 2⋅51 × 10 2 . NOTE that there appears to be 2 possible answers for the number 100, namely 1 × 10 2 or 10 × 10 1 . Only 1 × 10 2 is correct since we do not allow a 10 × .... etc. 2) a) 3.526 × 10 7 , b) 8.19 × 10 3 , c) 1 × 10 5 , d) 4⋅21544 × 10 6 , e) 2⋅0828571 × 10 4 , f) 4⋅2352941 × 10 1 , g) 8 × 10 7 , h) 2 × 10 9 , i) 4.6656 × 10 16 . Remember to put the brackets in part h). Also, beware of your calculator leaving out the ×10 ... etc. 3) a) 3500000, b) 0.0082. Comment regarding questions 4 and 5). NO CALCULATORS !!! These do not turn up frequently enough that you should be overly concerned if you find them difficult. Just be prepared to have a go. For example, (3 × 10 2 ) × (2 × 10 3 ) can be written (3 × 10 × 10) × (2 × 10 × 10 × 10) which simplifies to give the answer of 6 × 10 5 . (3 × 10 2 ) × (2 × 10 3 ) Simply staring at the questions in conjunction with the answers below might do the job! Failing that, ask your teacher ! 4) a) 6 × 10 5 , b) 8 × 10 6 , c) 9 × 10 8 , d) 6.2 × 10 10 , e) 8.6 × 10 8 , f) 9.6 × 10 3 , g) 9.9 × 10 −3 , h) 9.6 × 10 −5 , i) 6 × 10 3 . 5) a) 1.2 × 10 6 , b) 1.8 × 10 7 , c) 1.8 × 10 9 , d) 4 × 10 11 , e) 1.25 × 10 10 , f) 1.20 × 10 5 , g) 1.86 × 10 4 , h) 1.56 × 10 4 , i) 1.32 × 10 10 . ©www.mathsguru.co.uk
Page 1 and 2: INDICES and STANDARD FORM As mentio
Page 3 and 4: Easy enough ? To make things easier
Page 5: Example 4. Light travels at approxi

INDICES and STANDARD FORM

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