SAT-87: The Art of Estimation

SAT-87: The Art of Estimation

Description: You don't always need the exact answer to choose the right one. Estimation — rounding numbers to friendly values and doing quick mental math — gets you close enough to eliminate wrong choices and often pick the winner. It also catches silly mistakes on questions you do solve exactly.

The core moves

• Round ugly numbers to nearby friendly ones (98 → 100, 4.9 → 5, 1/3 → 0.33).
• Do the easy arithmetic with the rounded numbers.
• Pick the choice closest to your estimate; eliminate the far ones.

(Oʻzbekcha: sonlarni qulay qiymatlarga yaxlitlang, soʻng oson hisoblab, eng yaqin variantni tanlang.)

When estimation shines

It's ideal when the answer choices are spread far apart, or when a question only asks "about how many?" If two choices are very close together, estimate to narrow down, then compute exactly. (Oʻzbekcha: javoblar bir-biridan uzoq boʻlsa, baholash juda samarali.)

Worked Example 1 — round and multiply

Estimate 19.8 × 5.1. Choices: 25, 50, 100, 200.

• Round: 20 × 5 = 100. The closest choice is 100.

Worked Example 2 — percent estimate

About what is 48% of 802? Choices: 200, 400, 600, 800.

• 48% ≈ 50% = half; 802 ≈ 800; half of 800 = 400. Answer ≈ 400.

(Oʻzbekcha: 48% ni 50% (yarmi) deb, 802 ni 800 deb oling.)

Worked Example 3 — sanity-check an exact answer

You computed √215 and got 14.7. Is that reasonable?

• 14² = 196 and 15² = 225, so √215 must be between 14 and 15. 14.7 fits → reasonable.
• If you'd gotten 47 or 1.5, estimation would catch the error instantly.

Tip: even on "solve exactly" questions, a 5-second estimate before answering catches decimal-point and sign mistakes. (Oʻzbekcha: aniq yechgan javobni ham baholab tekshiring — xatolarni ushlaydi.)

Worked Example 4 — estimate a square root

About how big is √50? Choices: 5, 7, 12, 25.

• 50 is just above 49 = 7², so √50 is a little more than 7.
• Answer ≈ 7. (The trap 25 is 50 ÷ 2, and 5 would be √25.)

(Oʻzbekcha: 50 ≈ 49 = 7², shuning uchun √50 ≈ 7.)

Estimating with fractions

Fractions are easier to estimate if you turn them into rough decimals or compare them to ½. For instance, 5/9 is a bit more than ½, and 2/7 is a bit less than ⅓. So "5/9 of 60" is a little more than 30, and you can eliminate any choice far from that. Comparing a fraction to a familiar benchmark (½, ⅓, ¼) is often faster than exact division. (Oʻzbekcha: kasrlarni ½ yoki ⅓ kabi tanish qiymatlar bilan solishtirib baholang.)

Why estimation also saves time

Beyond catching errors, estimation can be the whole solution when choices are far apart — you never compute the exact value at all. The skill is knowing when "close enough" is enough: if the four choices are 5, 50, 500, and 5000, a rough estimate instantly picks the right power of ten. Save exact arithmetic for when two choices are genuinely close. (Oʻzbekcha: javoblar uzoq boʻlsa, baholashning oʻzi yetarli — aniq hisoblash shart emas.)

Practice 1

Estimate 31 × 9.8. Choices: 90, 150, 300, 600.

Practice 2

About what is 9.9% of 1,010? Choices: 1, 10, 100, 1000.

Key words — Kalit soʻzlar

• Estimate — taxminiy hisoblash
• Round — yaxlitlash
• Approximate — taxminiy
• About / Roughly — taxminan
• Sanity check — mantiqiy tekshiruv
• Mental math — ogʻzaki hisob
• Friendly number — qulay son
• Eliminate — chiqarib tashlash
• Reasonable — mantiqiy

Summary

• Round to friendly numbers, do quick mental math, pick the closest choice.
• Best when answer choices are far apart or the question says "about."
• Estimate even on exact problems to catch big mistakes.