To estimate the value of [tex]\(\frac{3.04 \times 1.98 - 9.48}{2.91}\)[/tex] by first rounding off each number to one significant figure, let's follow these steps:
1. Rounding Each Number:
- [tex]\(3.04\)[/tex] is rounded to [tex]\(3\)[/tex].
- [tex]\(1.98\)[/tex] is rounded to [tex]\(2\)[/tex].
- [tex]\(9.48\)[/tex] is rounded to [tex]\(9\)[/tex].
- [tex]\(2.91\)[/tex] is rounded to [tex]\(3\)[/tex].
2. Substituting the Rounded Numbers:
- Replace [tex]\(3.04\)[/tex] with [tex]\(3\)[/tex].
- Replace [tex]\(1.98\)[/tex] with [tex]\(2\)[/tex].
- Replace [tex]\(9.48\)[/tex] with [tex]\(9\)[/tex].
- Replace [tex]\(2.91\)[/tex] with [tex]\(3\)[/tex].
3. Perform the Calculation with the Rounded Numbers:
Now our expression is [tex]\(\frac{3 \times 2 - 9}{3}\)[/tex].
4. Calculating the Numerator:
- First, compute [tex]\(3 \times 2 = 6\)[/tex].
- Then, subtract [tex]\(9\)[/tex]: [tex]\(6 - 9 = -3\)[/tex].
5. Calculating the Denominator:
- The denominator is simply [tex]\(3\)[/tex].
6. Forming the Fraction and Calculating the Estimated Value:
- Our new expression becomes [tex]\(\frac{-3}{3}\)[/tex].
- Compute the division: [tex]\(\frac{-3}{3} = -1\)[/tex].
So, the estimated value of [tex]\(\frac{3.04 \times 1.98 - 9.48}{2.91}\)[/tex] is approximately [tex]\(-1.0\)[/tex].
