Accuracy and Significant Figures
Aligned to N-Q.A.3 — Common Core State Standards for Mathematics.
What this lesson teaches
A reported number should not claim more precision than the measurement allows. A ruler marked in millimeters cannot justify an answer to the nearest thousandth. When measurements are multiplied, round the result to the fewest significant figures of the inputs.
Worked examples
Example 1
A rectangle is measured as 4.2 cm by 7.0 cm. Area = 4.2 * 7.0 = 29.4 cm². Each measurement has 2 significant figures, so the area should also have 2: round 29.4 to 29 cm². Reporting 29.40 cm² would falsely suggest a more precise measurement than the ruler gave.
Example 2
A runner covers 400 m (measured to the nearest meter, 3 significant figures) in 52.4 seconds (3 significant figures). Speed = 400 / 52.4 = 7.6335... m/s. Both inputs carry 3 significant figures, so report 7.63 m/s. The calculator's extra digits are not measurements — they are arithmetic.
Example 3
Common mistake: treating addition like multiplication. For multiplication and division you keep the fewest SIGNIFICANT FIGURES; for addition and subtraction you keep the fewest DECIMAL PLACES. Adding 12.11 g + 0.3 g gives 12.41 on the calculator, but 0.3 is only good to one decimal place, so the sum is 12.4 g. Using the significant-figure rule here would wrongly keep 12.41.
Practice questions
- A length is measured as 3.6 m. How many significant figures does it have, and what is the smallest place value you should report?
- You measure a table as 1.25 m by 0.80 m. Compute the area and round to the correct number of significant figures.
- A digital scale reads 2.4 kg. Why would it be misleading to report a total of 12.00 kg for five such objects?
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Exactitud y cifras significativas
Un número reportado no debe afirmar más precisión de la que permite la medición. Una regla marcada en milímetros no justifica una respuesta al milésimo. Cuando se multiplican mediciones, redondea el resultado a la menor cantidad de cifras significativas de los datos.
Ejemplo 1: Un rectángulo se mide como 4.2 cm por 7.0 cm. Área = 4.2 * 7.0 = 29.4 cm². Cada medición tiene 2 cifras significativas, así que el área también debe tener 2: redondea 29.4 a 29 cm². Reportar 29.40 cm² sugeriría falsamente más precisión de la que dio la regla.
Ejemplo 2: Un corredor recorre 400 m (medidos al metro más cercano, 3 cifras significativas) en 52.4 segundos (3 cifras significativas). Rapidez = 400 / 52.4 = 7.6335... m/s. Ambos datos tienen 3 cifras significativas, así que se reporta 7.63 m/s. Los dígitos extra de la calculadora no son mediciones — son aritmética.
Ejemplo 3: Error común: tratar la suma como la multiplicación. En multiplicación y división se conserva la menor cantidad de CIFRAS SIGNIFICATIVAS; en suma y resta se conserva la menor cantidad de CIFRAS DECIMALES. Sumar 12.11 g + 0.3 g da 12.41 en la calculadora, pero 0.3 solo llega a un decimal, así que la suma es 12.4 g. Aplicar aquí la regla de cifras significativas conservaría 12.41 por error.
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