Answer:
1. State the number of significant digits in each measurement.
1) 2804 m = 4 significant digits
2) 2.84 km = 3 significant digits
3) 5.029 m = 4 significant digits
4) 0.003068 m = 4 significant digits
5) 4.6 x 10^5 m = 2 significant digits
6) 4.06 x 10^-5 m = 3 significant digits
7) 750 m = 2 significant digits
8) 75 m = 2 significant digits
9) 75,000 m = 2 significant digits
10) 75.00 m = 4 significant digits
11) 75,000.0 m = 6 significant digits
12) 10 cm = 1 significant digit
2. Round the following numbers as indicated:
To four figures:
3.6824172 = 3.682
1.86005137 = 1.860
5.652311 = 5.652
2.5114 = 2.511
5.4673 = 5.467
To one decimal place:
1.3511 = 1.4
2.473 = 2.5
5.687524 = 5.7
7.555 = 7.6
8.235 = 8.2
To two decimal places:
22.494 = 22.49
79.258 = 79.26
80.0306 = 80.03
23.4125 = 23.41
41.866323 = 41.87
Solve the following problems and report answers with appropriate number of significant digits.
1) 6.201 cm + 7.4 cm + 0.68 cm +12.0 cm = 26.281 cm (5 significant digits)
2) 1.6 km + 1.62 km +1200 km = 1203.22 km (6 significant digits)
3) 8.264 g - 7.8 g = 0.464 g (3 significant digits)
4) 10.4168 m - 6.0 m = 6.4168 (5 significant digits)
5) 12.00 kg+15.001 kg= 27.001 kg (5 significant digits)
6) 1.31 cm x 2.3 cm = 3.013 cm² (4 significant digits)
7) 5.7621 m x 6.201 m = 35.7307821 (9 significant digits)
8) 20.2 cm / 7.41 s = 2.726046 (7 significant digits)
Explanation
The significant digits of a number are the digits that have meaning or contribute to the value of the number. Sometimes they are also called significant figures.
Which digits are significant?
There are some basic rules that tell you which digits in a number are significant:
All non-zero digits are significant
Any zeros between significant digits are also significant
Trailing zeros to the right of a decimal point are significant
Which digits aren't significant?
The only digits that aren't significant are zeros that are acting only as place holders in a number. These are:
Trailing zeros to the left of the decimal point (note: these zeros may or may not be significant)
Leading zeros to the right of the decimal point
