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Welcome to GCSE Edexcel Maths revision.

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Topic M 5: Rounding, estimation and accuracy.

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This video covers Higher tier.

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It includes the shared content and the labelled Higher extensions.

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Decimal places count digits after the decimal point;

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significant figures start at the first non-zero digit. 0.004762 to 2 significant figures is 0.0048;

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to 3 decimal places it is 0.005.

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To round, inspect the next digit: 5 or more rounds up, less than 5 stays.

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Include trailing zeros when they communicate precision: 3.5 to 2 decimal places is 3.50.

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Truncation removes digits without rounding.

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Truncating 4.789 to 2 decimal places gives 4.78, while rounding gives 4.79.

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For positive measurements truncated to 4.78, 4.78 is less than or equal to x is less than 4.79.

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For a negative value truncated towards zero,

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the interval has the opposite included end: a value truncated to minus 4.78 at 2 decimal places satisfies minus 4.79 is less than x is less than or equal to minus 4.78.

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Distinguish truncation from rounding.

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Estimate by rounding inputs to convenient values,

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often one significant figure. the fraction with numerator open bracket 19.8 multiplied by 5.12 close bracket and denominator open bracket 0.49 close bracket ,

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end fraction is approximately equal to the fraction with numerator open bracket 20 multiplied by 5 close bracket and denominator open bracket 0.5 close bracket ,

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end fraction equals 200.

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An estimate checks the size, not the exact answer.

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Use standard units and convert before combining measurements. 2.3 metres plus 45 centimetres equals 2.75 metres, not 47.3 metres.

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A measured length rounded to 8.4 centimetres to the nearest 0.1 centimetres has interval 8.35 is less than or equal to l is less than 8.45 centimetres.

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Half the rounding step lies on each side of the reported value.

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Error interval for 8.4 centimetres

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The lower bound is included and the upper bound is excluded under the usual GCSE convention.

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Rounding 8.45 centimetres would give 8.5 centimetres, so it cannot be included in the interval for 8.4 centimetres.

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Worked example: A mass of 350 grams to the nearest 10 grams means 345 is less than or equal to m is less than 355 grams.

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A whole-number-looking measurement is not necessarily accurate to the nearest 1 gram.

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Limits of accuracy describe possible actual measurements; they are not probabilities and do not imply the reported measurement is always exactly in the middle.

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Give final answers to the requested precision and retain full calculator values during intermediate steps.

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Write is approximately equal to for rounded values, rather than joining unequal exact values with equals .

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For positive a and b, the largest possible a plus b uses both upper bounds and the smallest uses both lower bounds.

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For a minus b, the upper limit uses upper a minus lower b.

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For positive quantities, a product's upper limit uses both upper bounds.

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A quotient's upper limit uses the largest numerator and smallest denominator; its lower limit reverses those choices.

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Worked example: A rectangle is 8.4 centimetres by 5.2 centimetres, each to the nearest 0.1 centimetres.

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Its area lies between 8.35 multiplied by 5.15 equals 43.0025 square centimetres and 8.45 multiplied by 5.25 equals 44.3625 square centimetres , with the upper limit excluded.

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Worked example: Distance is 100 metres to the nearest metre and time is 20 seconds to the nearest second.

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Speed's lower limit is the fraction with numerator open bracket 99.5 close bracket and denominator open bracket 20.5 close bracket ,

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end fraction is approximately equal to 4.854 metres per second;

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upper limit is the fraction with numerator open bracket 100.5 close bracket and denominator open bracket 19.5 close bracket ,

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end fraction is approximately equal to 5.154 metres per second.

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Do not divide the two upper bounds to find maximum speed.

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Only report a precision guaranteed by the entire possible interval.

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If the bounds round differently to a given precision, that precision is not justified for a single certain rounded result.

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That completes Rounding, estimation and accuracy.

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Revisit the notes and test yourself on the revision website.