JOURNAL #9

Determine each of the following to be a pure substance, homogeneous mixture or a heterogenous mixture: Water Iron metal Sugar water

SCIENTIFIC CALCULATIONS- SIGNIFICANT FIGURES

TODAY’S LEARNING GOAL

Today, we will determine the amount of significant figures in a given number.

WHAT IS THE LENGTH OF THIS LEAF?

(assume this ruler is measuring in cm)

Significant figures are critical when reporting scientific data because they give the reader an idea of how well you could actually measure/report your data

Every measurement has a degree of uncertainty associated with it. The uncertainty derives from the measuring device and from the skill of the person doing the measuring.

1. ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are significant. • 613 has three sig figs• 123456 has six sig figs

2. ALL zeroes between non-zero numbers are significant.• 5004 has four sig figs• 602 has three sig figs• 6000000000000002 has 16

sig figs!

3. Trailing zeros are significant only if the number contains a decimal point; otherwise they are insignificant. Trailing zeros that aren't needed to hold the decimal point are significant. For example, 4.00 has three significant figures.

• 5.640 has four sig figs• 120000. has six sig figs• 120000 has two sig figs

4. Zeros to left of the first nonzero digit are insignificant

• 0.000456 has three sig figs• 0.052 has two sig figs• 0.00000000000000000000000000052 also has two sig

figs!

1. 48,9232. 3.9673. 900.064. 0.0004 (= 4 E-4)5. 8.10006. 501.0407. 3,000,000 (= 3 E+6)8. 10.0 (= 1.00 E+1)

Number # Significant Figures Rule(s)

48,923 5 1

3.967 4 1

900.06 5 1,2,4

0.0004 (= 4 E-4) 1 1,4

8.1000 5 1,3

501.040 6 1,2,3,4

3,000,000 (= 3 E+6) 1 1

10.0 (= 1.00 E+1) 3 1,3,4

JOURNAL #7 Identify the number of significant figures

for in the problems below:1. 456.232. .000253. 1.0024. 2360005. 1.0236. 4007. 4.5 x 108. 4.59. 30.110. 30111. 3010

ADDITION AND SUBTRACTION WITH SIGNIFICANT FIGURES

When combining measurements with different degrees of accuracy and precision, the accuracy of the final answer can be no greater than the least accurate measurement. 

When measurements are added or subtracted, the answer can contain no more decimal places than the least accurate measurement.

EXAMPLE OF ADDITION/ SUBTRACTION

1.7.939 + 6.26 + 11.1 = 25.299 (this is what your calculator spits out)

• In this case, your final answer is limited to one sig fig to the right of the decimal

• 25.3 (rounded up).

2.150.0 + 1.507 = 151.5

ROUNDING OFF When the answer to a calculation

contains too many significant figures, it must be rounded off.

There are 10 digits that can occur in the last decimal place in a calculation. One way of rounding off involves underestimating the answer for five of these digits (0, 1, 2, 3, and 4) and overestimating the answer for the other five (5, 6, 7, 8, and 9).

ROUNDING OFF

If the digit is smaller than 5, drop this digit and leave the remaining number unchanged. Thus, 1.684 becomes 1.68.

If the digit is 5 or larger, drop this digit and add 1 to the preceding digit. Thus, 1.247 becomes 1.25.

NOW IT’S YOUR TURN!

MULTIPLICATION AND DIVISION WITH SIGNIFICANT FIGURES The same principle governs the use of

significant figures in multiplication and division: the final result can be no more accurate than the least accurate measurement.

In this case, however, we count the significant figures in each measurement, not the number of decimal places.

When measurements are multiplied or divided, the answer can contain no more significant figures than the least accurate measurement.

EXAMPLECalculate the length in inches of a piece of wood 1.245 feet long. Determine the correct number of significant figures.

The original measurement (1.254 feet) has four significant figures, but there seem to be only two significant figures in the number of inches in a foot. Thus, it might seem that the answer should contain only two significant figures.

We can clear up this confusion by remembering that only measurements involve error or uncertainty. Many unit factors are based on definitions. For example, 1 foot is defined as exactly 12 inches. Unit factors based on definitions have an infinite number of significant figures. The answer to this problem therefore contains four significant figures.

EXAMPLE Calculate the length in inches of a

piece of wood 1.245 feet long. Determine the correct number of significant figures.

Answer:14.94 in

NOW IT’S YOUR TURN!

Practice for Quiz on Friday!!!!