Question

measurement can only be as accurate and precise as the instrument that produced it. a scientist must be able to express the accuracy of a number, not just its numerical value. we can determine the accuracy of a number by the number of significant figures it contains.

1. all digits 1 - 9 inclusive are significant. example: 129 has 3 significant figures.
2. zeros between significant digits are always significant. example: 5,007 has 4 significant figures.
3. trailing zeros in a number are significant only if the number contains a decimal point. example: 100.0 has 4 significant figures. 100 has 1 significant figure.
4. zeros in the beginning of a number whose only function is to place the decimal point are not significant. example: 0.0025 has 2 significant figures.
5. zeros following a decimal significant figure are significant. example: 0.000470 has 3 significant figures. 0.47000 has 5 significant figures.

determine the number of significant figures in the following numbers.

1. 0.02
2. 0.020
3. 501
4. 501.0
5. 5,000
6. 5,000.
7. 6,051.00
8. 0.0005
9. 0.1020
10. 10,001

determine the location of the last significant place value by placing a bar over the digit. (example: 1.700)

1. 8040
2. 0.0300
3. 699.5
4. 2.000×10²
5. 0.90100
6. 90,100
7. 4.7×10⁻⁸
8. 10,800,000.
9. 3.01×10²¹
10. 0.000410

Explanation:

Step1: Analyze 0.02

Zeros at the beginning to place the decimal are not significant. Only the 2 is significant, so it has 1 significant - figure.

Step2: Analyze 0.020

The leading zeros are not significant, but the zero after 2 is significant as it is after a non - zero digit in a decimal. So it has 2 significant figures.

Step3: Analyze 501

All non - zero digits and the zero between non - zero digits are significant. So it has 3 significant figures.

Step4: Analyze 501.0

All digits are significant. The zero after the decimal is significant. So it has 4 significant figures.

Step5: Analyze 5,000

There is no decimal point, so only the 5 is significant. It has 1 significant figure.

Step6: Analyze 5,000.

The decimal point makes the trailing zeros significant. So it has 4 significant figures.

Step7: Analyze 6,051.00

All digits are significant. So it has 6 significant figures.

Step8: Analyze 0.0005

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

Step9: Analyze 0.1020

The leading zero is not significant, but the other digits are. So it has 4 significant figures.

Step10: Analyze 10,001

All digits are significant. So it has 5 significant figures.

Answer:

1. 1
2. 2
3. 3
4. 4
5. 1
6. 4
7. 6
8. 1
9. 4
10. 5