I don't understand how to round to significant digits
565 lb * 30 ft
4900 ft/ 144 sec
786 hr * 23 miles per hour
The first one will be to one significant digit because of the 30 has only one sig digit.
The second will have two because of the numerator.
The third will have 2 because of the denominator.
I under stand this but once i get the answers i really don't know how to do it these re the answers i get
1. 16950
2. 34.02777778
3. 18078
but i don't understand how to round it like would the first one be 10?
Rounding to significant digits involves determining the number of digits in a number that are considered significant or important. To round to significant digits, follow these steps:
1. Identify the significant digits: Start by identifying the digits in the number that are non-zero. All non-zero digits are considered significant. For example, in the number 565 lb, all three digits (5, 6, and 5) are significant.
2. Determine the number of significant digits needed: Look at the precision requirement or the number of significant digits that you want to keep in the final answer. This may be specified in the question or in the context of the problem. For example, if the precision requirement is 2 significant digits, you would keep the first two digits from step 1.
3. Consider rounding rules: Now, you need to decide whether to round up or down. If the next digit after the desired number of significant digits is 5 or greater, you round up. If it is less than 5, you round down.
4. Adjust the number: Finally, adjust the number according to the rounding rule. If you are rounding up, increase the desired significant digits by 1. If you are rounding down, simply keep the desired significant digits.
Now, let's apply these steps to your examples:
1. 565 lb * 30 ft:
- In this case, the number of significant digits is not explicitly mentioned, so let's assume we want the result to have 2 significant digits.
- Multiply 565 by 30: 565 * 30 = 16,950.
- The first two significant digits are 1 and 6.
- Since the next digit (9) is 5 or greater, we round up.
- Therefore, the rounded result is 17,000 ft.
2. 4900 ft / 144 sec:
- Again, let's assume we want the answer to have 3 significant digits.
- Divide 4900 by 144: 4900 / 144 = 34.0277777778.
- The first three significant digits are 3, 4, and 0.
- The next digit (2) is less than 5, so we round down.
- Therefore, the rounded result is 34.0 ft/s.
3. 786 hr * 23 miles per hour:
- Assuming we want 4 significant digits in the answer, let's calculate.
- Multiply 786 by 23: 786 * 23 = 18,078.
- The first four significant digits are 1, 8, 0, and 7.
- Since the next digit (8) is 5 or greater, we round up.
- Therefore, the rounded result is 18,080 miles.
Remember, significant digits are used to reflect the precision or accuracy of a measurement or calculation. The rules for rounding may vary in some cases, so always pay attention to specific instructions or context.