Mathematics Higher Level Robert Joinson

©Sumbooks2002Higher Level2. Standard FormExercise 1Write down these numbers in standard form1) 457 2) 1427 3) 94314) 156,321 5) 17 million 6) 0.28137) 0.08142 8) 0.000486 9) 0.0000097Exercise 2Change these numbers from standard form1) 2.8 × 10 52) 6.4 × 10 73) 9.3 × 10 44) 4.315 × 10 65) 8.614 × 10 96) 4.31 × 10 27) 3.2 × 10 68) 6.84 × 10 79) 4.38 × 10 9Exercise 3Calculate each of the following leaving your answers in standard form. Round off to foursignificant figures wherever necessary.1) ( 6.4 × 10 2 ) × ( 3.8 × 10 4 )2) ( 5.4 × 10 6 ) × ( 8.3 × 10 2 )3) ( 4.6 × 10 2 ) × ( 3.4 × 10 3 )4) ( 4.3 × 10 7 ) × ( 8.8 × 10 5 )5) ( 8.3 × 10 2 ) × ( 6.4 × 10 8 )6) ( 5.3 × 10 7 ) × ( 4.6 × 10 3 )7) ( 5.7 × 10 2 ) ÷ ( 3.4 × 10 2 )8) ( 8.3 × 10 6 ) ÷ ( 5.4 × 10 3 )9) ( 8.4 × 10 5 ) ÷ ( 2.4 × 10 3 )10) ( 5.4 × 10 7 ) ÷ ( 4.3 × 10 2 )11) 137, 000 × 10 512) 0.08123 × 10 613) 27.31 × 4.82 × 10 614) 571.31 × 4.2 × 10 73.841 × 10 67.41 × 10 415) ---------------------------16)3.182 10 2--------------------------×3.54 × 10 6( 27.41 × 10 3 ) × ( 2.684 × 10 7 )( 2.641 × 10 3 ) × ( 2.84 × 10 6 )17) -----------------------------------------------------------------------18)7.41 10 5-------------------------------------------------------------------------×3.82 × 10 519) 4× 10 420) 9×10 6Exercise 41) The distance from the earth to a star is 8×10 13 kilometres. Light travels at a speed ofapproximately 3.0 × 10 5 kilometres per second.a) How far will light travel in one year?b) How long will light take to travel from the star to the earth? Give your answer correct to3 significant figures.2) The mass of the earth is 5.976 × 10 24 kilograms and the mass of the moon is 7.35 × 10 22kilograms.a) Write down these masses in tonnes.b) How many times is the mass of the earth greater than the mass of the moon?3) A neutron has a mass of 1.675 × 10 27 kilograms and an electron 9.109 × 10 31 kilograms.a) How many electrons are needed for their mass to be equal to that of a neutron?b) How many electrons are required to have a mass of 1 kg?