Using standard units with decimal quantities

Number • Measures and accuracy

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Explain when decimals are inappropriate for measurements.

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Decimals are inappropriate for counts of discrete items because counts require whole numbers, not fractional parts.

Key concepts

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Standard units and common prefixes

Standard units include kilogram (kg) for mass, metre (m) for length, second (s) for time, and pound or currency units for money. Prefixes change unit scale; kilo- multiplies by 1,000, centi- divides by 100, milli- divides by 1,000. Prefixes cause systematic shifts in decimal place position, which enables direct use of decimals for conversions. Prefixes have exact factors that limit rounding error; conversions must use the exact factor (for example, 1 kg = 1000 g) to avoid compound inaccuracies in later calculations.

Converting between units using decimals

Conversion proceeds by multiplying or dividing by the exact factor between units, producing decimal quantities when results are not whole numbers. For example, converting 1.75 kg to grams uses 1.75 × 1000 = 1750 g; converting 2500 m to kilometres uses 2500 ÷ 1000 = 2.5 km. Consistent unit choice prevents algebraic errors: convert all measurements to the same unit before addition or subtraction. Decimal notation simplifies arithmetic and maintains precision when using calculators.

Time and decimal hours

Time uses hours, minutes and seconds. Decimal hours express minutes and seconds as fractional parts of an hour: minutes divide by 60 and seconds divide by 3600. For example, 1 hour 30 minutes equals 1.5 hours because 30 ÷ 60 = 0.5. Decimal time simplifies rate calculations (distance ÷ time) but requires careful conversion when results need hours:minutes:seconds format, since decimal fractions of an hour correspond to minutes and seconds when multiplied by 60 or 3600.

Money and decimal notation

Currency commonly uses decimal notation to represent subunits (for example, pounds and pence, or dollars and cents). Decimal representation matches everyday transactions and calculator work: £3.75 represents 3 pounds and 75 pence, equivalent to 3 + 75/100. Rounding money follows currency smallest-unit rules (usually to two decimal places). Calculations that produce more decimal places require rounding to the appropriate currency precision before reporting totals.

Compound measures and unit consistency

Compound measures combine base units, such as speed (metres per second, m/s) or density (grams per cubic centimetre, g/cm³). Decimal representation commonly appears in compound measures when quantities are not whole numbers. Unit consistency matters: convert all parts of a compound measure to compatible units before calculation (for example, convert km/h to m/s by multiplying by 1000 then dividing by 3600, producing decimals). Failure to convert units causes incorrect results.

Rounding, accuracy and limiting factors

Rounding controls the stated precision of decimal measurements. Rounding to a given number of decimal places or significant figures prevents overstatement of precision. For example, a measurement stated as 2.30 m implies precision to the nearest centimetre, while 2.3 m implies less explicit precision. Measurement precision depends on the instrument and context. Decimal quantities are inappropriate for counts of discrete objects and are only meaningful when the measurement process supports the declared precision.

Key notes

Important points to keep in mind

Always convert all measurements to the same unit before adding or subtracting.

Use exact conversion factors (e.g., 1 kg = 1000 g) to avoid accumulating errors.

Express time as decimal hours by dividing minutes by 60 and seconds by 3600 for rate calculations.

Round results only to the precision justified by the measuring instrument or context.

Currency uses fixed smallest-unit rounding (usually two decimal places).

Convert both parts of a compound measure to compatible units before calculating.

Avoid decimal representation for counts of discrete objects.

Report units clearly with the numeric answer to preserve meaning.