Vocabulary: accuracy adjacent angle of depression angle of elevation area capacity composite figure cosine ratio cylinder error   field diagram hypotenuse opposite perimeter quadrant rate ratio right prism scale diagram scale factor scientific notation significant figures similar sine ratio standard prefix tangent ratio trigonometry unitary method volume

Basic concepts: repeat and average measurements to reduce the likelihood of error investigate the degree of accuracy of reported measurements, including the use of significant figures where appropriate use scientific notation and standard prefixes in the context of measurement express measurements in scientific notation calculate with ratios, including finding the ratio of two quantities, dividing quantities in a given ratio, and using the unitary method to solve problems calculate rates, including pay rates, rates of flow, and rates of speed convert between units for rates, eg km/h to m/s, mL/min to L/h convert between common units for area convert between common units for volume determine the overall change in a quantity following repeated percentage changes, eg an increase of 20% followed by a decrease of 20%.

Conversions Convert the following: 1. 5 km to m = 2. 2.4 m to cm = 3. 18 cm to mm = 4. 3 km to cm = 5. 27.6 m to mm = 6. 50 mm to cm = 7. 228 cm to m = 8. 8700 m to km = 9. 870 mm to m = 10. 640 000 cm to km =

1. mm to cm (divide by 10) 4. cm to mm (multiply by 10) a) 10 mm = ________ cm a) 4 cm = ______ mm b) 60 mm = ________ cm b) 10 cm = _____ mm c) 120 mm = _______ cm c) 50 cm = ______ mm d) 95 mm = ________ cm d) 120cm = _____ mm 2. cm to m ( divide by 100) 5. m to cm ( multiply by 100) a) 100 cm = ________ m a) 5 m = ______ cm b) 500 cm = ________ m b) 1 m = ______ cm c) 900 cm = ________ m c) 20 m = ______ cm d) 640 cm = ________ m d) 6.9 m = ______ cm 3. m to km ( divide by 1000) 6. km to m ( multiply by 1000) a) 1000 m = ________ km a) 1 km = ______ m b) 4000 m = ________ km b) 7 km = ______ m c) 9000 m = ________ km c)60 km = ______ m d) 3460 m = ________ km d) 5.8 km = _____ m

Error in Measurement When physically measuring, what causes error? If the ruler is not lined up properly If the ruler is inaccurate (calibration error) or if it is damaged If you are not looking at it ‘straight-on’ (parallax error) There is ALWAYS some error due to the limits of measuring instruments NOTE: When a scale is used correctly, the maximum possible error in the measurement is half (or 0.5) of the measurement unit used. It could be smaller or larger than the actual measurement. Some people record the measurement as  0.5. (an example of this might be saying a piece of wood is 107 cm long when it is actually 107.3 cm long)

Relative error gives an indication of how good a measurement is relative to the size of the quantity being measured. The relative error of a measurement is calculated by dividing the limit of reading by the actual measurement.

Significant Figures To express a number to a given number of significant figures: Start at the first non-zero digit (regardless of whether it occurs before or after the decimal point) Count the number of significant figures required. If the next digit is: 5 or more increase the number to the left by one and replace all following numbers with zeroes less than 5 leave the number to the left unchanged and replace all following numbers with zeroes. NOTE: all non-significant figures before the decimal point are replaced by zeroes; all non-significant figures after the decimal point are omitted.

Significant Figures Some examples: Round 8726 to: a) 2 significant figures 8700 b) 3 significant figures 8730 Round 0.002357 to: a) 1 significant figure 0.002 b) 3 significant figures 0.0024 c) 5 significant figures 0.0023570

Questions: 1. Write the following correct to a) one significant figure: b) two significant figures c) three significant figures 1) 3.2 2)453 3)2471 4)0.075 5) 47.3 6)0.000203

Scientific Notation Scientific Notation (Standard Form) is often used to express very large or small numbers as a power of 10. To write a number in scientific notation we perform the following steps: Place a decimal point so that the number appears to be between 1 and 10. Count how many decimal places your decimal point is from its old position.

Questions: 1. Write 3400 using scientific notation 2. Write 0.098 using scientific notation 3. Write 5.6734 x 102 as a basic numeral 4. Write 7.3 x 10-4 as a basic numeral 5. Calculate (4.5 x 103) x (3.2 x 102) 6. Calculate (7.6 x 1012) ÷ (4.0 x 103) 7. Calculate (2.5 x 104) x (3 x 1010) 6 x 103

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Prefixes used for large (and small) numbers A 'prefix' is attached to the front of a word to change its meaning. The prefixes in the table below indicate the factor of 10 by which the base unit is multiplied. For example 1 kilogram = 1000 grams (the gram is the base unit for mass)

Ratios A ratio is a comparison of numbers in a definite order. they are not, we need to convert one, or both, so that they are. To compare items, they need to be in the same units (mL, $, etc). If Ratios can be written in the form a:b or a to b. Ratios can be used to compare more than two numbers e.g. a:b:c

Solving Problems with Ratios A block model is often useful in solving problems.

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Rates

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Conversions between Units of Area To change from m2 to cm2 (or other units), you can draw a diagram and write the measurements on, or learn the conversion flowchart. (Similarly for volume conversions) e.g. How many cm2 in 1m2? 1 m 100 cm 1 m 1 m2 100 cm Area = 100 x 100 = 10 000 cm2

Percentage Change

Percentage Change

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