Question

significant figures worksheet

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

246.32 ________ 1.008 ______ 700000 ________
107.854 ________ 0.00340 ______ 350.670 ________
100.3 ________ 14.600 ______ 1.0000 ________
0.678 ________ 0.0001 ______ 320001 ________

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

32.567
135.0
+ 1.4567
__________
246.24
238.278
+ 98.3
__________
658.0
23.5478
+ 1345.29
__________

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

a) 23.7 x 3.8 = ________ e) 43.678 x 64.1 = ________
b) 45.76 x 0.25 = ________ f) 1.678 / 0.42 = ________
c) 81.04 x 0.010 = ________ g) 28.367 / 3.74 = ________
d) 6.47 x 64.5 = ________ h) 4278 / 1.006 = ________

Explanation:

Step1: Determine significant - figures rules

Non - zero digits are always significant. Zeros between non - zero digits are significant. Trailing zeros in a number with a decimal point are significant. Leading zeros are not significant. Trailing zeros in a whole number without a decimal point may or may not be significant, but in scientific work, they are often considered not significant.

Step2: Count significant figures for each value in part 1

• 246.32: 5 significant figures (all digits are non - zero or between non - zero digits).
• 1.008: 4 significant figures (zeros between non - zero digits are significant).
• 700000: 1 significant figure (trailing zeros in a whole number without a decimal point are not significant).
• 107.854: 6 significant figures.
• 0.00340: 3 significant figures (leading zeros are not significant, trailing zero after non - zero digits is significant).
• 350.670: 6 significant figures.
• 100.3: 4 significant figures.
• 14.600: 5 significant figures.
• 1.0000: 5 significant figures.
• 0.678: 3 significant figures.
• 0.0001: 1 significant figure.
• 320001: 6 significant figures.

Step3: Perform addition and round for part 2

• \(32.567+135.0 + 1.4567=169.0237\). Rounding to the least number of decimal places (1 decimal place from 135.0), the answer is 169.0.
• \(246.24+238.278 + 98.3=582.818\). Rounding to 1 decimal place (from 98.3), the answer is 582.8.
• \(658.0+23.5478+1345.29 = 2026.8378\). Rounding to 1 decimal place (from 658.0), the answer is 2026.8.

Step4: Perform multiplication/division and round for part 3

• \(23.7\times3.8 = 89.06\). Rounding to 2 significant figures (the least number of significant figures in the factors), the answer is 89.
• \(45.76\times0.25=11.44\). Rounding to 2 significant figures (from 0.25), the answer is 11.
• \(81.04\times0.010 = 0.8104\). Rounding to 2 significant figures (from 0.010), the answer is 0.81.
• \(6.47\times64.5 = 417.215\). Rounding to 3 significant figures (the least number of significant figures in the factors), the answer is 417.
• \(43.678\times64.1=2800.7598\). Rounding to 3 significant figures (from 64.1), the answer is 2800.
• \(1.678\div0.42 = 3.995238\). Rounding to 2 significant figures (from 0.42), the answer is 4.0.
• \(28.367\div3.74 = 7.58476\). Rounding to 3 significant figures (from 3.74), the answer is 7.58.
• \(4278\div1.006 = 4252.485\). Rounding to 4 significant figures (from 4278), the answer is 4252.

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) 89
b) 11
c) 0.81
d) 417
e) 2800
f) 4.0
g) 7.58
h) 4252