Question

here we will look at some guidelines to follow in determining whether or not digits in a measurement are significant. all digits are always significant. the zeros are a little more complex. we will use the terms \leading,\ \trailing,\ and \captive\ for the zeros and will consider how to deal with them. starting with the first digit on the left, count this digit and all remaining digits to the right. this is the number of significant figures in the measurement unless the last digit is a zero lying to the left of where the decimal point would be located. captive zeros result from and are therefore always significant. zeros, however, are never significant—they merely tell us where the decimal point is located. we could use exponential notation and express the number as ; then the number contains all of the significant figures, and locates the decimal point. the number of significant figures is uncertain in a number that ends with a zero to the left of the decimal point location. the ambiguity can be resolved with the use of in cases where only the decimal - formatted number is available, it is prudent to assume that all trailing zeros are significant figures worksheet for each of the following measurements, identify the correct number of significant figures. determine the presence of nonzero digits, leading zeros, captive zeros, and trailing zeros. consider whether the number includes a decimal point or not. 1. 1203.0 grams: 2. 5000 kilometers: 3. 0.03050 liters: 4. 100. grams: 5. 0.010 milliliters: 6. 3000000 watts: 7. 70.07 amps: 8. 0.0008001 seconds: 9. 0.005000 meters: 10. 200.0 volts: 11. 10.00 ohms 12. 40.00 newtons: 13. 0.004560 kilograms: 14. 9090.0 joules:

Explanation:

Step1: Recall significant - figure rules

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

Step2: Analyze 1203.0 grams

Non - zero digits 1, 2, 3 and captive zero 0 between 2 and 3, and trailing zero after decimal are significant. So there are 5 significant figures.

Step3: Analyze 5000 kilometers

Without a decimal point, the trailing zeros may or may not be significant. Assuming no additional information, there is 1 significant figure.

Step4: Analyze 0.03050 liters

Leading zeros are not significant. Non - zero digits 3, 5 and captive zero 0 between 3 and 5, and trailing zero after 5 are significant. So there are 4 significant figures.

Step5: Analyze 100. grams

The decimal point makes the trailing zeros significant. So there are 3 significant figures.

Step6: Analyze 0.010 milliliters

Leading zeros are not significant. Non - zero digit 1 and trailing zero after 1 are significant. So there are 2 significant figures.

Step7: Analyze 3000000 watts

Without a decimal point, there is 1 significant figure.

Step8: Analyze 70.07 amps

Non - zero digits 7, 7 and captive zeros 0 between 7 and 0, 0 between 0 and 7 are significant. So there are 4 significant figures.

Step9: Analyze 0.0008001 seconds

Leading zeros are not significant. Non - zero digits 8, 1 and captive zeros 0 between 8 and 1 are significant. So there are 4 significant figures.

Step10: Analyze 0.005000 meters

Leading zeros are not significant. Non - zero digit 5 and trailing zeros after 5 are significant. So there are 4 significant figures.

Step11: Analyze 200.0 volts

The decimal point makes the trailing zeros significant. So there are 4 significant figures.

Step12: Analyze 10.00 ohms

Non - zero digits 1 and trailing zeros after 1 are significant. So there are 4 significant figures.

Step13: Analyze 40.00 newtons

Non - zero digit 4 and trailing zeros after 4 are significant. So there are 4 significant figures.

Step14: Analyze 0.004560 kilograms

Leading zeros are not significant. Non - zero digits 4, 5, 6 and trailing zero after 6 are significant. So there are 4 significant figures.

Step15: Analyze 9090.0 joules

Non - zero digits 9, 9 and captive zero 0 between 9 and 9, and trailing zero after 9 are significant. So there are 5 significant figures.

Answer:

1. 5
2. 1
3. 4
4. 3
5. 2
6. 1
7. 4
8. 4
9. 4
10. 4
11. 4
12. 4
13. 4
14. 5