Question

part a: identification (problems 1 - 6)
instructions: determine the number of significant digits in each measurement.

1. 0.00456 g
2. 3.070 cm
3. 500 ml
4. 2.40×10⁴ kg
5. 0.0800 m
6. 1,205,000 atoms

part b: rounding (problems 7 - 12)
instructions: round each number to the specified number of significant digits.

1. round 45.678 to 3 significant digits
2. round 0.008934 to 2 significant digits
3. round 1,567,890 to 4 significant digits
4. round 23.456 to 2 significant digits
5. round 0.07845 to 3 significant digits
6. round 9.9999 to 3 significant digits

part c: addition and subtraction (problems 13 - 24)
instructions: perform the calculation and express your answer with the correct number of significant digits.

1. 12.45 + 3.2+0.678 =
2. 45.67 - 12.3 =
3. 123.4 + 56.78 - 9.123 =
4. 0.0456 + 1.23+0.789 =
5. 234.5 - 12.67 =
6. 0.123 + 45.6 + 2.34 =

Explanation:

Part A: Identification of Significant Digits

1. 0.00456 g

The leading zeros are not significant. So, there are 3 significant digits.

2. 3.070 cm

The zeros between non - zero digits and trailing zeros after a decimal point are significant. So, there are 4 significant digits.

3. 500 mL

If no decimal point is present, trailing zeros may or may not be significant. Assuming standard rules without further context, there is 1 significant digit.

4. 2.40×10⁴ kg

In scientific notation, all digits in the coefficient are significant. So, there are 3 significant digits.

5. 0.0800 m

Leading zeros are not significant, but trailing zeros after a non - zero digit and a decimal point are significant. So, there are 3 significant digits.

6. 1,205,000 atoms

Trailing zeros without a decimal point are not significant. So, there are 4 significant digits.

Part B: Rounding

7. Round 45.678 to 3 significant digits

The fourth digit is 7. Since 7≥5, we round up the third digit. So, 45.7.

8. Round 0.008934 to 2 significant digits

The third digit is 3. Since 3<5, we keep the first two non - zero digits. So, 0.0089.

9. Round 1,567,890 to 4 significant digits

The fifth digit is 8. Since 8≥5, we round up the fourth digit. In scientific notation, 1.568×10⁶.

10. Round 23.456 to 2 significant digits

The third digit is 4. Since 4<5, we keep the first two digits. So, 23.

11. Round 0.07845 to 3 significant digits

The fourth digit is 5. Since 5≥5, we round up the third digit. So, 0.0785.

12. Round 9.9999 to 3 significant digits

The fourth digit is 9. Since 9≥5, we round up the third digit. So, 10.0.

Part C: Addition and Subtraction

13. 12.45+3.2 + 0.678

First, add the numbers: 12.45+3.2+0.678 = 16.328. The least number of decimal places among the numbers being added is 1 (in 3.2). So, we round to 16.3.

14. 45.67−12.3

Subtract: 45.67−12.3 = 33.37. The least number of decimal places among the numbers is 1 (in 12.3). So, we round to 33.4.

15. 123.4+56.78−9.123

First, add 123.4 and 56.78: 123.4+56.78 = 180.18. Then subtract 9.123: 180.18−9.123 = 171.057. The least number of decimal places is 1 (in 123.4). So, we round to 171.1.

16. 0.0456+1.23+0.789

Add: 0.0456+1.23+0.789 = 2.0646. The least number of decimal places is 2 (in 1.23). So, we round to 2.06.

17. 234.5−12.67

Subtract: 234.5−12.67 = 221.83. The least number of decimal places is 1 (in 234.5). So, we round to 221.8.

18. 0.123+45.6+2.34

Add: 0.123+45.6+2.34 = 48.063. The least number of decimal places is 1 (in 45.6). So, we round to 48.1.

Answer:

1. 3 significant digits
2. 4 significant digits
3. 1 significant digit
4. 3 significant digits
5. 3 significant digits
6. 4 significant digits
7. 45.7
8. 0.0089
9. 1.568×10⁶
10. 23
11. 0.0785
12. 10.0
13. 16.3
14. 33.4
15. 171.1
16. 2.06
17. 221.8
18. 48.1