Solving Number Problems US5235 Solving Number Problems

SIGNIFICANT FIGURES - Count from the first non-zero number e.g. State the number of significant figures (s.f.) in the following: a) 7553 b) 4.06 c) s.f. 3 s.f. 2 s.f. Zero’s at the front are known as place holders and are not counted - A way of representing numbers DECIMAL PLACES - Count from the first number after the decimal point e.g. State the number of decimal places (d.p.) in the following: a) d.p. - Another way of representing numbers b) d.p. c) 460 d.p.

ROUNDING 1. DECIMAL PLACES (d.p.) i) Count the number of places needed AFTER the decimal point ii) Look at the next digit - If it’s a 5 or more, add 1 to the previous digit - If it’s less than 5, leave previous digit unchanged iii) Drop off any extra digits e.g. Round to: a) 1 decimal place (1 d.p.)b) 4 d.p. Next digit =2 = leave unchanged = 6.1 Next digit =8 = add 1 = The number of places you have to round to should tell you how many digits are left after the decimal point in your answer. i.e. 3 d.p. = 3 digits after the decimal point. When rounding decimals, you DO NOT move digits

2. SIGNIFCANT FIGURES (s.f.) i) Count the number of places needed from the first NON-ZERO digit ii) Look at the next digit - If it’s a 5 or more, add 1 to the previous digit - If it’s less than 5, leave previous digit unchanged iii) If needed, add zeros as placeholders to keep the number the same size e.g. Round to: a) 1 significant figure (1 s.f.)a) 2 s.f. Next digit =2 = leave unchanged = 6.1 Next digit =7 = add 1 = 19 e.g. Round to: 000 Don’t forget to include zeros if your are rounding digits BEFORE the decimal point. Your answer should still be around the same place value - ALWAYS round sensibly i.e. Money is rounded to2 d.p.

FRACTIONS 1. SIMPLIFYING FRACTIONS - Fractions must ALWAYS be simplified where possible e.g. Simplify a) 5 = 10 b) 6 = 9 c) 45 = Make use of the a b/c button on your calculator - When fraction has been entered into calculator, simply press equals 2. CALCULATIONS INVOLVING FRACTIONS - Enter calculation as seen in question using the fraction button a) = b) ×= 4 e.g. Simplify

3. MIXED NUMBERS and IMPROPER FRACTIONS - Mixed numbers are combinations of whole numbers and fractions. e.g. Change into improper fractions: a) 3 4 b) = = To change into an improper fraction use d/c button. (shift key and a b/c button) - Improper fractions have the top number bigger than the bottom.

PERCENTAGES 1. ONE AMOUNT AS A PERCENTAGE OF ANOTHER - A number of similar strategies such as setting up a fraction and multiplying by 100 exist. e.g. Paul got 28 out of 50. What percentage is this? 100 ÷ 50 = 2(each mark is worth 2%) 28 × 2 = 56% e.g. Mark got 39 out of 50. What percentage is this? × 100 = 78%

- To calculate percentage increase/decrease we can use: Percentage increase/decrease = decrease/increase × 100 original amount e.g. Mikes wages increased from $11 to $13.50 an hour. a) How much was the increase? b) Calculate the percentage increase = $ × 100= 22.7%(1 d.p.) e.g. A car originally brought for $4500 is resold for $2800. What was the percentage decrease in price? Decrease = $1700 = Percentage Decrease= × 100 = 37.8%(1 d.p.) 2. PERCENTAGE INCREASE/DECREASE To spot these types of questions, look for the word ‘percentage’

3. WORKING OUT ORIGINAL QUANITIES - Convert the final amount’s percentage into a decimal. - Divide the final amount by the decimal. e.g. 16 is 20% of an amount. What is this amount e.g. A price of $85 includes a tax mark-up of 15%. Calculate the pre-tax price. 20% as a decimal =0.2 Amount =16÷ 0.2 = 80 Final amount as a percentage = =115 Final amount as a decimal =1.15 Pre-tax price =85÷ 1.15 = $73.91 To spot these types of questions, look for words such as ‘pre’, ‘before’ or ‘original’

RATIOS - Compare amounts of two quantities of similar units - Written with a colon - Can be simplified just like fractions and should always contain whole numbers e.g. Simplify 200 mL : 800 mL ÷200 1 mL : 4 mL e.g. Simplify 600 m : 2 km Must have the same units! 600 m : 2000 m ÷200 3 m : 10 m

2. SPLITTING IN GIVEN RATIOS - Steps:i) Add parts ii) Divide total into amount being split iii) Multiply answer by parts in given ratio e.g. Split $1400 between two people in the ratio 2:5 e.g. What is the smallest ratio when $2500 is split in the ratio 5:3:2 Total parts:2 + 5= 7 Divide into amount:1400 ÷ 7= 200 Multiply by parts:200 × 2= $ × 5= $1000 Answer: $400 : $1000 Order of a ratio is very important Total parts: = 10 Divide into amount:2000 ÷ 10 Multiply by parts:250 × 2= $500 Answer: $500 = 250

PROPORTIONS - If less for 1, divide then multiply. - If more for 1, multiply then divide. e.g. If 4 oranges cost $3.60, how much will 9 cost? It costs less money for 1 orange so divide then multiply 3.60 ÷ 4 = × 0.90 =$8.10 e.g. If it takes 6 painters 15 days to paint a school, how long will it take for 10? It takes more time for 1 painter so multiply then divide 6 × 15 =90 90 ÷ 10 =9 days

ESTIMATION - Involves guessing what the real answer may be close to by working with whole numbers e.g. Estimate a) × =b) 413 × 2.96 =5 × 7400 × 3 = 35 = Generally we round numbers to 1 significant figure first