📝 Round Decimals in Algebra (13 MCQs)

📖 From Digital SAT Algebra • 1. Basics of Algebra • 13 questions available

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What is Round Decimals in Algebra?

Definition:
Rounding decimals in algebra means reducing the number of decimal places based on a specified place value, by looking at the digit to the right of the target place: if it is $5$ or more, round up (increase the target digit by 1), otherwise round down (keep target digit), and drop all digits to the right.

Working:
Identify the place to round to (e.g., tenths, hundredths), look at the next digit to the right; if it's $\ge 5$ , add 1 to the target digit; if $< 5$ , leave it; then truncate all digits after the target place, keeping the decimal point.

Example:
Round $4.567$ to the nearest tenth.
Solution: Target is tenths place (5), next digit is 6 (which is $\ge 5$ ), so round up: $4.6$ .

Reason:
Rounding decimals is used to estimate results, make numbers easier to work with, and report answers with appropriate precision in scientific measurements, financial calculations, and algebraic solutions.

Easy

Medium

Hard

📝 All Round Decimals in Algebra MCQs

Q1. A school records a runner's time as $12.746$ seconds but reports times to the nearest tenth. Which value should appear in the final report?

12.7

seconds ✅

12.8

seconds

12.75

seconds

13.0

seconds

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: To round $12.746$ to the nearest tenth, identify the tenths digit, which is $7$ , and examine the hundredths digit, which is $4$ . Since $4$ is less than $5$ , the tenths digit remains unchanged, giving $12.7$ seconds.

Q2. A measuring device gives three readings: $4.263$ , $4.251$ , and $4.298$ meters. If all readings must be reported to the nearest hundredth, which sequence is correct?

4.26,\ 4.25,\ 4.29

4.27,\ 4.26,\ 4.30

4.26,\ 4.25,\ 4.30

✅

4.30,\ 4.25,\ 4.29

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: For each measurement, inspect the thousandths digit because the hundredths place is being retained. Thus $4.263$ becomes $4.26$ , $4.251$ becomes $4.25$ , and $4.298$ becomes $4.30$ because $8$ rounds the hundredths digit upward.

Q3. A number line is marked at $5.1,\ 5.2,\ 5.3,$ and $5.4$ . A point representing $5.26$ lies between $5.2$ and $5.3$ , slightly closer to $5.3$ . To the nearest tenth, where should the point be reported?

A.5.2

B.5.3 ✅

C.5.26

D.5

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: The point $5.26$ lies between $5.2$ and $5.3$ . Its hundredths digit is $6$ , which is at least $5$ , so the tenths digit $2$ increases to $3$ . Therefore, the rounded value is $5.3$ .

Q4. A carpenter measures a board as $18.675$ cm. The measurement must be recorded to the nearest hundredth. Another worker claims the answer is $18.67$ because the thousandths digit is $5$ and therefore the number should remain unchanged. Which response is most accurate?

A.The worker is correct because

5

never changes a digit.

B.The worker is correct because only digits greater than

5

cause rounding.

C.The worker is incorrect because a following digit of

5

causes the hundredths digit to increase, giving

18.68

. ✅

D.The worker is incorrect because the number must always be rounded to the nearest whole number.

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: When rounding to the nearest hundredth, the hundredths digit is $7$ , and the next digit is $5$ . Under the standard rounding rule, a digit of $5$ causes the retained digit to increase by one, producing $18.68$ .

Q5. A science experiment records a quantity as $0.0496$ . The teacher asks students to round it first to the nearest thousandth and then round that result to the nearest hundredth. What final value should they obtain?

A.0.04

B.0.05 ✅

C.0.05

D.0.06

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: First round $0.0496$ to the nearest thousandth. The thousandths digit is $9$ , and the next digit is $6$ , so the result becomes $0.050$ . Rounding $0.050$ to the nearest hundredth gives $0.05$ , since the hundredths digit is already $5$ .

Q6. Two students round $9.949$ to the nearest tenth. Student A says $9.9$ because the hundredths digit is $4$ . Student B says $10.0$ because the final digit is $9$ . Which conclusion is correct?

A.Student A, because the hundredths digit determines rounding and

4<5

. ✅

B.Student B, because any

9

forces the whole number upward.

C.Both students are correct because

9.949

is equally close to

9.9

and

10.0

D.Neither student is correct because the number should be

9.94

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: To round to the nearest tenth, inspect the hundredths digit, which is $4$ . Since $4<5$ , the tenths digit remains $9$ , producing $9.9$ . The final digit $9$ is irrelevant because it is not immediately after the rounding place.

Q7. A delivery truck travels $27.864$ km, but the report requires the distance to the nearest tenth. Which value should be recorded, and why?

27.8

, because

4<5

27.9

, because the hundredths digit

6

increases the tenths digit ✅

28.0

, because the decimal contains more than two digits

27.86

, because two decimal places are always required

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: The target place is the tenths position, which contains $8$ . The next digit is the hundredths digit $6$ , so the tenths digit must increase from $8$ to $9$ . Therefore, the correctly rounded distance is $27.9$ km.

Q8. A laboratory records a mass of $14.375$ grams and requires measurements rounded to the nearest hundredth. A student reports $14.37$ . Which analysis best identifies the student's mistake?

A.The student should examine the thousandths digit

5

, which causes the hundredths digit to increase, giving

14.38

. ✅

B.The student should examine the tenths digit

3

, giving

14.40

C.The student should remove all digits after the hundredths place without changing anything.

D.The student should round to the nearest whole number first.

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: The hundredths digit is $7$ , and the digit immediately following it is $5$ . Because the next digit is $5$ , the retained hundredths digit increases from $7$ to $8$ . Thus $14.375$ rounds to $14.38$ .

Q9. A store lists a product price as $8.496$ dollars but displays prices to the nearest cent. A customer argues that the displayed price should be $8.49$ because the third decimal digit is $6$ , which is not part of the cents value. What should the cashier display?

A.8.49

B.8.5 ✅

C.8.496

D.9

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The nearest cent means rounding to the hundredths place. In $8.496$ , the hundredths digit is $9$ , and the thousandths digit is $6$ , so the value rounds upward. This creates a carry, changing $8.49$ to $8.50$ .

Q10. A number-line point is located at $3.74$ , between $3.7$ and $3.8$ . When rounding to the nearest tenth, which labeled value should represent the point?

3.7

, because

3.74

is less than

3.75

✅

3.8

, because

3.74

has a hundredths digit of

4

3.7

, because the tenths digit must never change

3.8

, because every decimal between

3.7

and

3.8

rounds upward

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: The target is the nearest tenth, so the hundredths digit determines the rounding. Since $3.74$ has $4$ in the hundredths position, the tenths digit remains $7$ . Therefore, the point rounds to $3.7$ , not $3.8$ .

Q11. A student rounds $6.2497$ first to the nearest hundredth and then independently to the nearest tenth. Which pair of results is correct?

6.24

and

6.2

6.25

and

6.2

✅

6.25

and

6.3

6.20

and

6.3

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: For the nearest hundredth, inspect the thousandths digit $9$ , so $6.24$ becomes $6.25$ . For the nearest tenth, inspect the hundredths digit $4$ , so the tenths digit remains $2$ , giving $6.2$ . Therefore, the correct pair is $6.25$ and $6.2$ .

Q12. A technician measures three wires as $2.146$ m, $2.154$ m, and $2.149$ m. The measurements must be reported to the nearest hundredth. Which report preserves the required precision?

2.15,\ 2.15,\ 2.15

2.14,\ 2.15,\ 2.14

✅

2.15,\ 2.16,\ 2.15

2.1,\ 2.2,\ 2.1

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: For $2.146$ , the thousandths digit $6$ makes the hundredths digit $4$ become $5$ , giving $2.15$ . For $2.154$ , the next digit is $4$ , so it stays $2.15$ . For $2.149$ , the $9$ raises $4$ to $5$ , giving $2.15$ .

Q13. A contest compares two methods for rounding $5.999$ to the nearest tenth. Method A looks only at the tenths digit and gives $5.9$ . Method B examines the hundredths digit before rounding and gives $6.0$ . Which method is mathematically justified?

A.Method A, because the digit being retained should never change.

B.Method A, because

9

in the tenths place means the value stays below

6

C.Method B, because the hundredths digit

9

causes a carry through the tenths place, producing

6.0

. ✅

D.Neither method, because decimals ending in

9

cannot be rounded.

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: To round $5.999$ to the nearest tenth, the hundredths digit $9$ requires the tenths digit $9$ to increase. That creates a carry into the whole-number part, changing $5.9$ into $6.0$ . Method B correctly accounts for this carry.

🔗 Related Topics (MCQs)

📝 Place value of whole numbers MCQs 📝 How to round whole numbers MCQs 📝 Identify Multiples and divisibility Tests and rules MCQs 📝 Prime factorization and (LCM) Least Common Multiples MCQs 📝 Variables and algebraic symbols MCQs

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