To round the number 473678 to three significant figures, follow these detailed steps:
1. Identify the Significant Figures:
- Significant figures are the digits that carry meaning contributing to its precision. For the number 473678, we will consider the first three significant digits only for rounding purposes.
2. Determine the Order of Magnitude:
- The order of magnitude provides the power of 10 to represent the scale of the largest significant figure in the number. For 473678, it is in the range of hundred-thousands, which corresponds to [tex]\(10^5\)[/tex].
3. Calculate the Rounding Factor:
- To round the number to three significant figures, we need to identify the place value of the third significant digit. Here, the third significant digit is 3, and it is in the thousands place (10^3). Therefore, the rounding factor here is 1000.
4. Perform the Rounding Operation:
- To round 473678 to three significant figures:
- First, divide the number by the rounding factor: [tex]\( 473678 \div 1000 = 473.678 \)[/tex].
- Next, round the result to the nearest whole number: [tex]\( 473.678 \approx 474 \)[/tex].
- Finally, multiply back by the rounding factor: [tex]\( 474 \times 1000 = 474000 \)[/tex].
Thus, when we round 473678 to three significant figures, the result is 474000.
To summarize:
- The order of magnitude of 473678 is 10^5.
- The rounding factor for three significant figures is 1000.
- The number 473678 rounded to three significant figures is 474000.
