A x 10 n, where 1 ^ A < 10 and n is an integer. ]

Transcription

1 WEST SPRING SECONDARY SCHOOL "THIRST FOR KNOWLEDGE" Name: WORKSHEET 6 ( ) Class: Date: Chapter 1: Indices and Standard Form Standard Form Very (arge and very small numbers are tedious to write. A system was developed to overcome this problem. It is called the Standard Form or Scientific Notation. A number in Standard Form is in the form of: A x 10 n, where 1 ^ A < 10 and n is an integer. ] -HM-. WMMMMMM IMMMMH Some examples are: 7.24x10" 1.258x x10- Converting Ordinary Form to Standard Form We live in a universe of different shapes and sizes. Ordinary Notation Standard Form 1 Light Year (Distance travelled by light in 1 year) Diameter of Sun Diameter of Earth m m m q.4&* ^ r* \-3ft x \# *.?1 x lo 1 ^ Length of Great Wall of China m -4- x \&^ ^ Height of a Soldier 1.7m I.~\ x \O r» Length of a mosquito Length of a Red Blood Cell 0.01 m m 1 x /o"* rn t-5 x 'o~ 6 ryi

2 Converting Standard Form to Ordinary Form ( Height of Mount Everest Length of a Marathon xofdid^cy^loution 8.848xl0 3 m xl0 4 m rsuadawlftapn- 5M r* p Diameter of the Moon 8.48xl0 6 m 3A-$O 000 ryo Diameter of Jupiter Length of a Bacterium Size of a HIV Radius of a Hydrogen Atom xlo'm 2xlO~ 6 m 9xlO- 8 m 2.5xl(T u m J4-2 %4 t>oo m 0- bbv 002. no 0- boo Cot? 0 [ rr\ 0- OOP w 0*0 025 rn Summary The following tables state the differences in the conversion of numbers to Standard Form and how lo recognise from Standard Form whether a number is greater or smaller than one. Conversion of Number to Standard Form HBMKwA*l**t Size of Number Directional Shift of Result on Index of : Decimal Point-; :- Base;10 wtthiadh.shift ; **^«.^%MP8^3CS!-«ii'.-fiBiE*-it,uxW &iivii*f-^ki-i i -- n>~rk\- -\f\i~ tr i rmrfimn itrl Greater than one (> 1) Left + 1 Smaller than one (< 1) Right - 1 The index of base 10 in a Standard Form helps us to recognise if a number is greater or smaller than one: Size of Number Greater than one (> 1) Smaller than one (< 1) Index of Base 10 Positive Negative Example x x1(T Converting from Standard Form When expressing a number in Standard Form as ordinary notation we do the reverse: Index of Base 10 Positive Negative Conversion of Standard Form to Number Directional Shift of Decimal Point Right Result on Index of Base 10 with each shift - 1 Left + 1

3 Example 1: Express in ordinary notation: The diameter of Mars = x10 6 m II) Distance travelled by light in one hour: 6.22x10 m II!) Average width of a strand of human hair: 8xlO~ 5 m Common SI Prefixes 10" Prefix Symbol Name Decimal Tera T Trillion Giga G Billion " Mega M Million io- 3 Kilo M1U1 K m Thousand Thousandth " 6 io- 9 Micro Nano M n Millionth Billionth IO- 12 Pico P Trillionth T G M tera giga mega, Mi 10' 10' METRIC PREFIX SCALE k m jji kilo (none) mil It micro nano pico IO ' 6 1,-12 1 IO' 1 ID" 2 hecto deca deci centi h da d c Tip: How to remember The Golden Monkey Kiss My Mama N^ Papa Tera Giga Mega Kilo Mill! Micro Nano Pico

4 1 The speed of light is given as 3.00 * 10 8 m/s. (a) The distance from Sun to Venus is 1.08 x 10" m. How long does light take to travel from the Sun to Venus? Express your answer in seconds. (b) If light takes 760 secondsto travel from the Sun to Mars, what is the distance from the Sun to Mars? Express your answer in standard form. 2. The base area of a rectangle tank is 3 x 10 5 cm 2 where its width and height are 4 x 10 2 cm and 5 x 10 3 cm respectively. Showing your working clearly and leaving your answers in standard form, calculate (a) its volume, (b) its length. 3. The population of China in 2007 is approximately 1.30 x The population of Thailand in 2007 is approximately 6.50x10'. (a) Express the population of Thailand as a percentage of the population of China. (b) How many more people live in China than in Thailand in 2007? Leave your answer in standard form. 4. One astronomical unit (AU) is equivalent to 150 gigametres. (a) Express 150 gigametres in metres, giving your answer in standard form. (b) Given that the speed of light to be 3 x 10 8 mis, how many seconds does light take to travel 1 AU? 5. The mass of a certain atom is 43 nanograms. (a) Write 43 nanograms in grams using standard form. (b) A container contains 4 billion atoms. Find the total mass in grams, of the atoms in the container. 6. Given that a = 3xlO and 6 = 9x10, find the value of -- ^, giving your answer in standard a~v 2 form. Homework: PRACTICE IF

5 SCHOOL.. CLASS DATE. NAME/INDEX NO... IF b O d;? <? ><=> ^ C. X 723-4^ * T o-a- = -4. lo - /. O2 -Jfl y O-118 X ~.46 X /o" J2-3 / 0 s y /o "q.2-7 T ^5 x o i±j* = o I5eis

6 SCHOOL. CLASS DATE _ NAME/INDEX NO... 6%* ^~ /O =- \o X /o = i ox I & > x /O h *) v to-* n/>i V vrt /i A. S \5o x

7 SCHOOL CLASS _ DATE _ NAME/INDEX NO 10 J) L >&& &c?c> X 000 x/c?"' a /o' 4 " 'X h ^ P.&& ?4-X/C>"" x fo - 7 r -4-f ^ /C?"' 2 - M ^ 7 X 42 fk*- "fxa*-^- ^S»A <^s%r- r (^ x ;ox 3; x -- - f tfeis

8 SCHOOL CLASS DATE _. NAME/INDEX NO 3 =*- 3P- - \o* \o~'~ n - f ~" '"^ /I ^ y \O m ~ I & X ^ 't-x XV 11 IJ - I / A-» i^^> "II * -w' -? - I V J /S* ' t/\s> 'I C-^^t- /vii I) 6**^^- " -^ i s^ I {/ = 4 X /C7 tf V 3- / h V x x ~ y I5eis

9 SCHOOL CLASS _ DATE _. NAME/INDEX NO lot) \OQ x fo ill -1-5 X 1C?' 3