Before you read

Answer first — see what you already know.

Estimate $83$ . Between which two integers does it fall?

A
8 and 9
B
9 and 10
C
7 and 8
D
10 and 11

Check your answer

Answer:

Before you read

Answer first — see what you already know.

A shirt costs $39.95. With 7% tax, the total is approximately:

A
$40
B
$42.75
C
$46.95
D
$50

Check your answer

Answer:

Theory

When to Estimate

Estimation is powerful on the ACT because:
1. The ACT is time-pressured (60 questions in 60 minutes)
2. Answer choices are often spread apart
3. Estimation can eliminate 2-3 wrong answers instantly

Strategies:
- Round to friendly numbers: $297 \times 4 \approx 300 \times 4 = 1200$
- Use benchmarks: $\sqrt{50}$ is between $\sqrt{49} = 7$ and $\sqrt{64} = 8$ , closer to 7
- Percent estimation: 15% of $82 ≈ 10% + 5% = $8.20 + $4.10 = $12.30
- Order of magnitude: Is the answer in the tens, hundreds, or thousands?

$√(48) ≈ ?$
$√(49) = 7$ nearest perfect square
$√(48) ≈ 6.93$ slightly less than 7

Estimation strategy: use nearby perfect squares

Estimating square roots on a number line

Example 1

Estimate $\frac{398 \times 52}{201}$

$\approx \frac{400 \times 50}{200} = \frac{20000}{200} = 100$

\approx

100 (exact: 102.98...)

Tip

ACT Pro Tip

If the answer choices are $45, $112, $380, and $1,200, you can often eliminate 2-3 options just by estimating the order of magnitude. This is especially useful when you're running low on time — a smart estimate beats a random guess.

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