1. **State the problem:** We want to approximate $1.98^{10}$ using the first five terms of the binomial expansion of $(1+x)^n$ where $n=10$ and $x$ is chosen such that $1+x=1.98$. 2. **Identify values:** Here, $n=10$ and $x=1.98-1=0.98$. 3. **Recall the binomial expansion formula:** $$ (1+x)^n = \sum_{k=0}^n \binom{n}{k} x^k = 1 + nx + \frac{n(n-1)}{2!}x^2 + \frac{n(n-1)(n-2)}{3!}x^3 + \frac{n(n-1)(n-2)(n-3)}{4!}x^4 + \cdots $$ 4. **Calculate the first five terms:** - Term 0: $1$ - Term 1: $10 \times 0.98 = 9.8$ - Term 2: $\frac{10 \times 9}{2} \times (0.98)^2 = 45 \times 0.9604 = 43.218$ - Term 3: $\frac{10 \times 9 \times 8}{6} \times (0.98)^3 = 120 \times 0.941192 = 112.94304$ - Term 4: $\frac{10 \times 9 \times 8 \times 7}{24} \times (0.98)^4 = 210 \times 0.92236816 = 193.6962936$ 5. **Sum these terms:** $$ 1 + 9.8 + 43.218 + 112.94304 + 193.6962936 = 360.6573336 $$ 6. **Interpretation:** Using the first five terms of the binomial expansion, $1.98^{10} \approx 360.66$. 7. **Note:** This is an approximation; including more terms would improve accuracy.