Question

1. verify that each of the following numbers contains four significant figures. circle the digits that are significant.

a) 0.00004182 b) 494,100,000 c) 32,010,000,000 d) 0.00003002

1. how many significant figures are in each of the following numbers?

__ a) 0.000015045 b) 4,600,000 __ c) 2406
__ d) 0.000005 e) 0.0300001 __ f) 12,000
copyright 2002 - 2004 by jason neil. all rights reserved. to make copies permission must be obtained from www.chemistryinquiry.com

Explanation:

Step1: Recall significant - figure rules

Non - zero digits are always significant. Zeros between non - zero digits are significant. Leading zeros (zeros before the first non - zero digit) are not significant. Trailing zeros in a number without a decimal point may or may not be significant. Trailing zeros in a number with a decimal point are significant.

Step2: Analyze 1(a) 0.00004182

The leading zeros are not significant. The non - zero digits 4, 1, 8, 2 are significant. So it has 4 significant figures.

Step3: Analyze 1(b) 494,100,000

The non - zero digits 4, 9, 4, 1 are significant. The remaining zeros are trailing zeros without a decimal point and are not considered significant in terms of the four - significant - figure requirement. So it has 4 significant figures.

Step4: Analyze 1(c) 32,010,000,000

The non - zero digits 3, 2, 0, 1 are significant. The remaining zeros are trailing zeros without a decimal point and are not considered significant in terms of the four - significant - figure requirement. So it has 4 significant figures.

Step5: Analyze 1(d) 0.00003002

The leading zeros are not significant. The non - zero digits 3, 0, 0, 2 are significant. So it has 4 significant figures.

Step6: Analyze 2(a) 0.000015045

The leading zeros are not significant. The non - zero digits 1, 5, 0, 4, 5 are significant. So it has 5 significant figures.

Step7: Analyze 2(b) 4,600,000

The non - zero digits 4, 6 are significant. The trailing zeros without a decimal point are not significant. So it has 2 significant figures.

Step8: Analyze 2(c) 2406

All digits (2, 4, 0, 6) are significant. So it has 4 significant figures.

Step9: Analyze 2(d) 0.000005

The leading zeros are not significant. Only the non - zero digit 5 is significant. So it has 1 significant figure.

Step10: Analyze 2(e) 0.0300001

The leading zeros are not significant. The non - zero digits 3, 0, 0, 0, 0, 1 are significant. So it has 6 significant figures.

Step11: Analyze 2(f) 12,000

The non - zero digits 1, 2 are significant. The trailing zeros without a decimal point are not significant. So it has 2 significant figures.

Answer:

1.

• a) Significant digits: 4, 1, 8, 2
• b) Significant digits: 4, 9, 4, 1
• c) Significant digits: 3, 2, 0, 1
• d) Significant digits: 3, 0, 0, 2

2.

• a) 5
• b) 2
• c) 4
• d) 1
• e) 6
• f) 2