Question

significant figures worksheet

1. indicate how many significant figures there are in each of the following measured values.

246.32 5
1.008 4/2
700000 1
107.854 6
0.00340 3
350.670 6
100.3 4
14.600 5
1.0000 1
0.678 3
0.0001 1
320001 6/3

1. calculate the answers to the appropriate number of significant figures.

32.567
135.0
+ 1.4567
169.0237
246.24
238.278
+ 98.3
582.818
658.0
23.5478
+ 1345.29
2016.8378

1. calculate the answers to the appropriate number of significant figures.

a) 23.7 x 3.8 = 90.1
e) 43.678 x 64.1 = 2800
b) 45.76 x 0.25 = 11.44
f) 1.678 / 0.42 = 4.00
c) 81.04 x 0.010 = 1
g) 28.367 / 3.74 = 7.58
d) 6.47 x 64.5 = 417.5
h) 4278 / 1.006 = 4252

Explanation:

Step1: Determine significant - figures rules

Non - zero digits are always significant. Zeros between non - zero digits are significant. Leading zeros are not significant. Trailing zeros are significant if there is a decimal point.

Step2: Count significant figures for part 1 values

246.32: 5 (all non - zero digits and digit between non - zero digits). 1.008: 4 (non - zero digits and zeros between non - zero digits). 700000: 1 (no decimal point, only the first non - zero digit is significant). 107.854: 6 (all digits). 0.00340: 3 (non - zero digits and trailing zero after non - zero digits). 350.670: 6 (all digits). 100.3: 4 (non - zero digits and zero between non - zero digits). 14.600: 5 (all digits). 1.0000: 5 (all digits). 0.678: 3 (all non - zero digits). 0.0001: 1 (only non - zero digit). 320001: 6 (all digits).

Step3: For addition/subtraction in part 2

The answer should be rounded to the least number of decimal places among the values being added or subtracted.
32.567+135.0 + 1.4567=169.0237, rounded to 169.0 (135.0 has one decimal place).
246.24+238.278+98.3 = 582.818, rounded to 582.8 (98.3 has one decimal place).
658.0+23.5478+1345.29 = 2026.8378, rounded to 2026.8 (658.0 has one decimal place).

Step4: For multiplication/division in part 3

The answer should have the same number of significant figures as the value with the least number of significant figures in the calculation.
a) 23.7×3.8 = 90.06, rounded to 90.1 (3.8 has 2 significant figures).
b) 45.76×0.25 = 11.44, rounded to 11 (0.25 has 2 significant figures).
c) 81.04×0.010 = 0.8104, rounded to 0.81 (0.010 has 2 significant figures).
d) 6.47×645 = 4173.15, rounded to 4170 (645 has 3 significant figures).
e) 43.678×64.1 = 2800.7598, rounded to 2800 (64.1 has 3 significant figures).
f) 1.678÷0.42 = 3.995238, rounded to 4.0 (0.42 has 2 significant figures).
g) 28.367÷3.74 = 7.585, rounded to 7.59 (3.74 has 3 significant figures).
h) 4278÷1.006 = 4252.485, rounded to 4250 (1.006 has 4 significant figures, but 4278 has 4 non - zero digits and we consider the least significant figures rule, and round to 4250).

Answer:

1. 246.32: 5; 1.008: 4; 700000: 1; 107.854: 6; 0.00340: 3; 350.670: 6; 100.3: 4; 14.600: 5; 1.0000: 5; 0.678: 3; 0.0001: 1; 320001: 6
2. 169.0; 582.8; 2026.8
3. a) 90.1; b) 11; c) 0.81; d) 4170; e) 2800; f) 4.0; g) 7.59; h) 4250