The Meaning Behind Significant Figures

When we record a number in science, we must indicate the precision of the measurement by using the correct number of significant figures. The general rule is to record to l/10 of the smallest division in the scale of the measuring device. For Ruler I below, the smallest division is 0.1cm. One-tenth of 0.1cm is 0.01cm. Thus measurements using Ruler I should be recorded to 0.01cm (two decimal places.) For Ruler II, however, the smallest division is 1cm. One-tenth of 1cm is 0.1cm. Thus, measurements using Ruler II should be recorded to 0.1cm (one decimal place).

Thus, Object A, measured with Ruler I should be recorded as ________________.

but as measured with Ruler II should be recorded as _______________.

(Write down your answers on paper before checking the answers provided below.)

Object B, measured with Ruler I is _______________

Object B, measured with Ruler II is _______________

(Write down your answers on paper before checking the answers provided below.)

Examine the three rulers. Which ruler gives the most precision? ____________

Which ruler gives the least accuracy? Why? ____________

For Ruler IV below, what is its smallest division? _________

How should measurements using Ruler IV be recorded (to how many decimal places)? ________

Ruler IV

cm

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Answers to above questions:

Object A, measured with Ruler I is 6.78 cm or 6.79 cm. The last digit may vary from person to person.

Object A, measured with Ruler II is 6.6 cm or 6.7 cm. The last digit may vary from person to person.

Object B, measured with Ruler I is 4.46 cm or 4.47 cm. The last digit may vary from person to person.

Object B, measured with Ruler II is 4.3 cm or 4.4 cm. The last digit may vary from person to person.

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Ruler I is the most precise because it has finer graduations. You can read to 0.01 cm.

Ruler III is the least accurate because the divisions are not equally spaced.

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If the object lies “exactly” on three on the ruler, the question arises as to how it should be recorded. Should it be recorded as 3cm, 3.0cm, or 3.00cm? It would depend on which ruler you use. Remember the rule that you record to l/10 of the smallest division.

The correct answers are: 3.00 cm with Ruler I, 3.0 cm with Ruler II, 3.0000 cm with Ruler IV.

(See Brady & Senese 5^th Ed, p.18 Sec 1.6)

(See Silberberg, 4^th Ed, Study Sec 1.6 & do p.36 #70)