When 25.302 is divided by 56.743, the answer should be reported to ____ significant digit(s).
The result of the division, 25.302 / 56.743, reported to the correct number of significant digits is _______
When 56.743 is subtracted from 25.302, the result should be reported with ____ digit(s) after the decimal point.
The difference, 25.302 - 56.743, reported to the correct number of significant digits is _____
To determine the number of significant digits in a division or subtraction problem, we need to understand the rules for significant digits.
1. Division:
When dividing numbers, the result should have the same number of significant digits as the term with the fewest significant digits.
In the given problem, 25.302 is divided by 56.743. Let's determine the number of significant digits in both numbers:
- The number 25.302 has five significant digits because all digits except the leading zero are significant.
- The number 56.743 has five significant digits as well, as all non-zero digits are significant.
Since both numbers have the same number of significant digits (five), the result of the division should also have the same number of significant digits.
Therefore, the answer to the first question is "5 significant digit(s)."
Now, let's perform the division:
25.302 ÷ 56.743 = 0.4455 (rounded to four decimal places)
The result, 0.4455, should be reported to four decimal places because it matches the number of significant digits specified.
Therefore, the answer to the second question is "0.4455."
2. Subtraction:
When subtracting numbers, the result should have the same number of decimal places as the term with the fewest decimal places.
In the given problem, 56.743 is subtracted from 25.302. Let's determine the number of decimal places in both numbers:
- The number 25.302 has three decimal places because there are three digits following the decimal point.
- The number 56.743 also has three decimal places.
Since both numbers have the same number of decimal places (three), the result of the subtraction should also have the same number of decimal places.
Therefore, the answer to the third question is "3 digit(s) after the decimal point."
Now, let's perform the subtraction:
25.302 - 56.743 = -31.441
The result, -31.441, should be reported with three digits after the decimal point because it matches the number of decimal places specified.
Therefore, the answer to the fourth question is "-31.441."