Estimating Decimals & Percents - Pre Algebra

1. Round each factor to the nearest whole number. What is the estimate of $7.9 \times 3.2$?

   $24$. The estimate is $8 \times 3$.

2. Without multiplying, is $1.2 \times 50$ greater than or less than $50$, and why?

   Greater. Multiplying a positive number by a factor greater than $1$ increases it (the product is $60$).

3. Use the benchmark $50\%$. What is the estimate of $49\%$ of $86$?

   $43$. Half of $86$ is $43$.

4. Round $3.92$ to $4$ and $0.51$ to $0.5$. What is the estimate of $3.92 \div 0.51$?

   $8$. There are $8$ halves in $4$.

5. Use $25\%$ and $80$. What is the estimate of $24.6\%$ of $81$?

   $20$. $25\%$ is $\frac{1}{4}$, and $\frac{1}{4}$ of $80$ is $20$.

6. Use $50\%$ and $200$. What is the estimate of $52\%$ of $198$?

   $100$. Half of $200$ is $100$.

7. A bill is 39.80 dollars. Rounding the bill to 40 dollars, what is the estimate of a 15% tip?

   6 dollars. 10% of 40 is 4 and 5% is 2, so 15% is about 6.

8. Use $\frac{1}{3}$ for $33\%$ and $60$ for $61$. What is the estimate of $33\%$ of $61$?

   $20$. One third of $60$ is $20$.

9. Round the percent to the nearest ten percent. What is the estimate of $19\%$ of $400$?

   $80$. Use $20\%$ of $400 = 0.2 \times 400$.

10. A student finds $0.6 \times 0.5 = 3$. What estimate shows this is unreasonable?

    Both factors are less than $1$, so the product must be less than $1$. The correct product is $0.3$.

11. Without multiplying, why must $0.98 \times 45$ be a little less than $45$?

    Multiplying a positive number by a factor slightly less than $1$ gives a result slightly less than the number.

12. Round each number to the nearest whole number. What is the estimate of $19.7 + 5.4 - 3.1$?

    $22$. The estimate is $20 + 5 - 3$.

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