Significant Figures and Measurements

Significant figures originally come from measurements. When measuring, you may estimate one decimal place beyond what the measuring device shows.
When you do this, then:
â€¢ All digits in your measurement are significant except place-holder zeroes.
â€¢ The last estimated digit is significant but uncertain.

Example 1: Measuring a Camera's Width With a Ruler Showing Centimeters
Say you are measuring the width of this camera with a ruler that only showed centimeters (cm).

 We can estimate this camera's width as, for example:
 We cannot estimate this camera's width as, for example:
 1 place past cm.6.5 cm
or
 1 place past cm.6.6 cm
 2 places past cm.6.57 cm
or
 2 places past cm.6.58 cm
 The last digit is significant but uncertain and is in the tenths place.Note: Technically we could say the width is 6.0, 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, or 6.9. But 6.4 and 6.5 look the closest to me.
 We're trying to go two decimal places beyond cm, to hundredths of a cm. Scientists donâ€™t allow estimates this accurate using this particular ruler.
 2 sig figs are allowed here.
 3 sig figs are NOT allowed.

Example 2: Measuring a Camera's Width With a Ruler Showing Tenths of a Centimeter.
Say you are measuring the same camera but now with a ruler that shows tenths of a centimeter.

We can estimate this camera's width as,  for example:
We cannot estimate this camera's width as,  for example:
 1 place past tenth of a cm.6.56 cm
or
 1 place past tenth of a cm.6.57 cm
 2 places past tenths of a cm.6.567 cm
or
 2 places past tenths of a cm.6.568 cm
 The last digit are significant but uncertain.Note: Technically we could estimate the width as 6.50, 6.51, 6.52, 6.53, 6.54, 6.55, 6.56, 6.57, 6.58, or 6.59. But 6.54 and 6.55 look the closest to me.
 Weâ€™re trying to go two decimal places beyond tenths of a cm to thousandths of a cm. Scientists donâ€™t trust estimates this accurate using this particular ruler.
 3 sig figs are allowed here.
 4 sig figs are NOT allowed.

Note: When using sig figs to measure, you can get zeroes at the end of decimals that are significant.

Example 3: The Measurement 7.0 cm. Normally, you wouldn't write 7.0 because it means the same thing as 7. As numbers, these mean the same thing. (There's no need to add the zero after the decimal.)
However, a measurement of 7.0 means something different from 7. It has two sig figs instead of one and is more accurate.
 As numbers, these mean the same thing.

7.0
 But as measurements they mean different thingsbecause...
7.0
 This has 1 sig fig. So it's less accurate
 This has 2 sig figs. So it's more accurate
 This measurement is accurate to the ones place. So it was made using a ruler that only showed tens of centimeters.The "7 was estimated" one place beyond what's showing.
 This measurement is accurate to the tenths place. So it was made using a ruler that only showed ones of centimeters. The "0 was estimated" one place beyond what's showing.
People who saw this lesson also found the following lessons useful:
 Significant Figures Place Holder Zeroes Determining Number of Significant Figures in Answer Scientific Notation and Significant Figures Significant Figures and Conversion Factors

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