When you are multiplying two numbers, how do you determine the number of significant figures?
You go with the lowest sig figs in your problem. so suppose you multiply 2.34 and 8.9574, in your product you should have 3 sig figs as the lowest sig fig in your problem is 2.34 which is 3 sig figs.
hope this helps.
how many sig figs are in 0.000 0250?
how many sig figs are in 45 000 000?
how many sig figs are in 7 210?
how many sig figs are in 273.15?
how many sig figs are in 200 000.0?
how many sig figs are in 7 000 000?
how many sig figs are in 0.052 4?
how many in 10? how many in 0.003 4?
how many in 98.6?how many in 0.005 0?
how many in 30.0? how many in 0.008 0?
3
2
3
5
7
1
3
1 and 2
3 and 2
3 and 2
just eat the pie and all will be well
To determine the number of significant figures in a given number, follow these rules:
1. Non-zero digits are always significant. For example, in 0.000 0250, all the non-zero digits (2, 5) are significant.
2. Leading zeros (zeros before any non-zero digits) are not significant. For example, in 0.000 0250, the leading zeros are not significant.
3. Captive zeros (zeros between non-zero digits) are significant. For example, in 45 000 000, all the zeros are significant.
4. Trailing zeros (zeros after non-zero digits and after the decimal point) are significant. For example, in 7 210, there are three significant figures.
5. Trailing zeros without a decimal point (zeros at the end of a whole number without any non-zero digits after) may or may not be significant. In the case of 200 000.0, the zero after the decimal point indicates that it is significant.
6. If a number is expressed in scientific notation, all digits in the coefficient are significant. For example, in 7 000 000, there are two significant figures.
Applying these rules to the given numbers:
- 0.000 0250 has three significant figures (2, 5, 0 after the decimal point).
- 45 000 000 has two significant figures (non-zero digits).
- 7 210 has three significant figures (non-zero digits).
- 273.15 has five significant figures (all digits are non-zero).
- 200 000.0 has seven significant figures (leading zeros are not significant, trailing zeros after the decimal point are significant).
- 7 000 000 has one significant figure (leading zeros are not significant).
- 0.052 4 has three significant figures (non-zero digits).
- 10 has one significant figure (non-zero digit).
- 0.003 4 has two significant figures (non-zero digits).
- 98.6 has three significant figures (all digits are non-zero).
- 0.005 0 has two significant figures (non-zero digits).
- 30.0 has three significant figures (all digits are non-zero).
- 0.008 0 has two significant figures (non-zero digits).
To determine the number of significant figures (sig figs) in a given number, follow these rules:
1. Non-zero digits are always significant. For example, in the number 273.15, there are 5 sig figs because each digit (2, 7, 3, 1, and 5) is non-zero.
2. Zeros between non-zero digits are always significant. For example, in the number 200 000.0, there are 7 sig figs because even though there are zeros at the beginning and end, the zeros between the non-zero digits (2, and 1) are significant.
3. Leading zeros (zeros before the first non-zero digit) are not significant. For example, in the number 0.000 0250, there are 3 sig figs because only the non-zero digits (2, 5, and 0) are significant.
4. Trailing zeros (zeros after the last non-zero digit) may or may not be significant depending on whether they are specified or measured. For example, in the number 45 000 000, it is unclear whether the trailing zeros are significant or not. Therefore, the number of sig figs is ambiguous in this case. However, if the number was written as 45 000 000.0, then it would have 8 sig figs because the trailing zero is specified.
Now let's apply these rules to the numbers you provided:
- 0.000 0250: There are 3 sig figs because the leading zeros are not significant, but the non-zero digits (2, 5, and 0) are significant.
- 45 000 000: The number of sig figs is ambiguous since it's unclear whether the trailing zeros are significant or not.
- 7 210: There are 4 sig figs because all the digits (7, 2, 1, and 0) are non-zero and there are no trailing zeros.
- 273.15: There are 5 sig figs because all the digits (2, 7, 3, 1, and 5) are non-zero.
- 200 000.0: There are 7 sig figs because the zeros between the non-zero digits and the trailing zero are significant.
- 7 000 000: There are 1 sig fig because the leading and trailing zeros are not significant, and there is only one non-zero digit (7).
- 0.052 4: There are 3 sig figs because the leading zero is not significant, but the non-zero digits (5, 2, and 4) are significant.
- 10: There is 1 sig fig because there is only one non-zero digit (1).
- 0.003 4: There are 2 sig figs because the leading zeros are not significant, and the non-zero digits (3 and 4) are significant.
- 98.6: There are 3 sig figs because all the digits (9, 8, and 6) are non-zero.
- 0.005 0: There are 2 sig figs because the leading zero is not significant, but the non-zero digits (5 and 0) are significant.
- 30.0: There are 3 sig figs because all the digits (3, 0, and 0) are non-zero and the trailing zero is specified.
- 0.008 0: There are 2 sig figs because the leading zero is not significant, and the non-zero digits (8 and 0) are significant.
Remember, these rules can help you determine the number of significant figures in any given number.