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1.10 Applying number

Syllabus
2017
Topic
1.10
Level
Foundation

Apply number in everyday decisions

Applying number means translating a real situation into quantities, operations and constraints, then interpreting the result in the original context.

Stage Question to ask
identify What is known, unknown and constrained?
standardise Do units, currencies or time formats need conversion?
calculate Which operations and order model the situation?
interpret Must the result be rounded up, rounded down or stated with units?

A budget cannot exceed the available money; a required number of journeys, packs or workers is normally rounded up; a number of complete items cut from material may need rounding down.

Estimate first, keep units beside intermediate quantities, and check whether the final value is realistic and satisfies every condition.

A mathematically correct decimal can still be an invalid practical answer. Context determines whether fractional items are possible and how rounding should be handled.

Calculate with metric units

Metric calculations require compatible units. Convert every measurement to a chosen common unit before adding, comparing or using a formula.

Quantity Key equivalence
length 1extm=100extcm=1000extmm1 ext{ m}=100 ext{ cm}=1000 ext{ mm}
mass 1extkg=1000extg1 ext{ kg}=1000 ext{ g}
capacity 1extlitre=1000extml1 ext{ litre}=1000 ext{ ml}
area 1extm2=10000extcm21 ext{ m}^2=10000 ext{ cm}^2
volume 1extm3=1000000extcm31 ext{ m}^3=1000000 ext{ cm}^3

Area conversion factors are squared and volume conversion factors are cubed. Since 1extm=100extcm1 ext{ m}=100 ext{ cm}, 1extm3=1003extcm31 ext{ m}^3=100^3 ext{ cm}^3.

A 10extmimes2.4extmimes2.4extm10 ext{ m} imes2.4 ext{ m} imes2.4 ext{ m} container holds 40extcm=0.4extm40 ext{ cm}=0.4 ext{ m} cubes in counts 25imes6imes6=90025 imes6 imes6=900 when aligned with its edges.

Do not use the linear factor 100 for area or volume. Also, a volume ratio alone may not prove that boxes fit; check whole-number edge counts and orientation.

Calculate with time, money and currencies

Time and money calculations depend on place-value systems and conversion rates. State the direction of every conversion before multiplying or dividing.

Job Method
elapsed time convert to one unit or bridge across clock times
money total align decimal places and round final currency to the smallest unit
currency conversion multiply by target units per source unit; divide to reverse
value comparison convert to one currency and compare cost per common unit

If 11 dollar =6.57=6.57 krone, dollars to krone uses imes6.57imes6.57 and krone to dollars uses ÷6.57\div6.57.

For competing oil offers, calculate litres per dollar or cost per litre after converting both prices into the same currency; only then compare value.

Time is not base 100: 2.752.75 hours is 22 hours 4545 minutes, not 22 hours 7575 minutes. A currency rate must be applied in the stated direction.