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8th Math: The Number System practice questions and exam guide

Name: 8th Math: The Number System exam prep
Author: CoStudy

150 multiple-choice questions and 83 flashcards, organised into 2 chapters, written to the CCSS Mathematics blueprint. Every question carries a full rationale.

Last reviewed 2026-10-26 · CoStudy · how we write and review questions

233 total items
150 multiple choice
83 flashcards
2 chapters

Study 8th Math: The Number System in CoStudy →

About the 8th Math: The Number System exam

CCSS Mathematics, Grade 8: Number System (8.NS.A.1-2) and integer exponents (8.EE.A.1). Public standards from corestandards.org.

CoStudy's 8th Math: The Number System bank holds 233 items organised into 2 chapters that follow the published blueprint. Every multiple-choice question carries a written rationale explaining why the correct answer is correct and why each distractor is tempting but wrong.

What the 8th Math: The Number System bank covers

Each chapter follows a domain of the published exam outline. Practise one on its own (chapter URLs are in the app and on this page for navigation; they are not sitemap targets):

Free 8th Math: The Number System practice questions

A sample of 12 multiple-choice questions from the bank, with the full rationale shown.

Which is RATIONAL?

1/4
π
√7
Not a real number

Answer: A — 1/4

A) Fractions of integers are rational. B/C) Non-repeating, non-terminating decimals — irrational. D) Imaginary.

Locate √50 on the number line. It is closest to:

Answer: D — 7.1

D) √50 ≈ 7.07, closest to 7.1. B) Halfway between 7 and 8 — too large. C) That's √64. A) Took half of 50.

Which is NOT a perfect square?

Answer: C — 50

√50 is not an integer (≈7.07), so 50 is not a perfect square. (A) 7² = 49; (B) 9² = 81; (D) 12² = 144.

Convert 2/9 to decimal:

0.18
0.2
0.222... (repeating)
0.29

Answer: C — 0.222... (repeating)

C) Repeating. A/B/D) Each is incorrect.

Square root of 0:

0
1
Undefined
Random

Answer: A — 0

A) Standard. B/C/D) Each is incorrect.

Negative exponent: 2⁻³ =

−8
1/8
8
0

Answer: B — 1/8

B) Reciprocal. A/C/D) Each is incorrect.

Which is the LARGEST?

√15
3.9
π + 1
√14

Answer: C — π + 1

C) π + 1 ≈ 4.14, largest. A) √15 ≈ 3.87. B) 3.9. D) √14 ≈ 3.74. Common error: pick √15 since the root looks 'big'.

Is π rational?

Yes
No — π is irrational (non-terminating, non-repeating decimal)
Sometimes
Unknown

Answer: B — No — π is irrational (non-terminating, non-repeating decimal)

B) Standard. A/C/D) Each is incorrect.

On a number line marked in tenths, √13 would be placed near:

Answer: A — 3.6

A) 3.6² = 12.96 ≈ 13. B) That's √10. C) That's √16 — off-by-one trap. D) Half of 13 — wrong operation.

Locate √11 on a number line. It falls between:

2 and 3
3 and 4
4 and 5
5 and 6

Answer: B — 3 and 4

B) 3² = 9 and 4² = 16; since 9 < 11 < 16, √11 ≈ 3.32. A) That's √4 to √9. C) That's √16 to √25 (off-by-one). D) Too large.

Order from greatest to least: √50, 7, 7.5, √40.

7.5, √50, 7, √40
√50, 7.5, 7, √40
√40, 7, 7.5, √50
√50, 7, 7.5, √40

Answer: A — 7.5, √50, 7, √40

A) √50 ≈ 7.07; √40 ≈ 6.32. So 7.5 > √50 ≈ 7.07 > 7 > √40 ≈ 6.32. B) Puts √50 above 7.5 — wrong. C) Reverse order. D) Wrong placement.

Which is closest to √70 on a number line?

Answer: B — 8.4

8² = 64 and 9² = 81. √70 ≈ 8.37. (A) 8.1² ≈ 65.6; (B) 8.4² ≈ 70.6 ✓; (C) 8.6² = 73.96; (D) 7.8² = 60.8.

8th Math: The Number System flashcards

6 sample cards from the 83 in the bank.

Is 0.121212... rational?

Yes — every repeating decimal is rational (here it equals 12/99 = 4/33).

Convert 1/8 to a decimal.

0.125.

Worked example: Convert 0.444... to a fraction.

Step 1: Let x = 0.444... . Step 2: Multiply both sides by 10 → 10x = 4.444... . Step 3: Subtract the original: 10x − x = 4.444... − 0.444... = 4. Step 4: This gives 9x = 4. Step 5: Divide both sides by 9 → x = 4/9. Answer: 0.444... = 4/9.

Is √2 rational or irrational?

Irrational. Its decimal goes on forever without repeating.

Is √7 rational?

No — √7 is irrational (7 isn't a perfect square).

Is π rational or irrational?

Irrational. 3.14159265... never terminates or repeats.

Practise the full 8th Math: The Number System bank

These samples are a small slice. The full bank runs flashcards, multiple choice and timed mock exams with per-chapter progress tracking, on the web and in the iOS app.

Open 8th Math: The Number System →

8th Math: The Number System — frequently asked

What is the 8th Math: The Number System exam?

CCSS Mathematics, Grade 8: Number System (8.NS.A.1-2) and integer exponents (8.EE.A.1). Public standards from corestandards.org.

How is CoStudy’s 8th Math: The Number System bank organised?

It holds 233 items across 2 chapters: Rational and Irrational Numbers; Approximating Irrational Numbers on the Number Line. Free samples on this page include the full rationale, with no account. Chapter counts in the bank are our mix; they are not a promise that the live exam uses the same item counts.

Does CoStudy replace the certifying body?

No. the certifying body owns the outline, the badge, and the sitting rules. This is independent practice with written rationales. We do not sell live items and we do not guarantee a pass.

Where do 8th Math: The Number System fees, cut scores, and pass rates live?

On the certifying body’s site. CoStudy will not invent a sitting fee or a pass rate. If a table on this page lacks a citation, treat it as unverified.

Are these real 8th Math: The Number System exam questions?

No. CoStudy does not have live items. The samples below are original practice written to the published outline, with rationales. Anyone selling “real exam dumps” is describing something you should not buy.

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