📝 Decimals in Algebra (7 MCQs)

📖 From Digital SAT Algebra • 1. Basics of Algebra • 7 questions available

←Previous Topic:Evaluate Variable Expressions with Fractions📝 Decimals in AlgebraReading and writing decimals:Next Topic→

What is Decimals in Algebra?

Definition:
Decimals in algebra are numbers that have a fractional part represented after a decimal point, based on powers of ten, and they are used similarly to integers and fractions in algebraic expressions, requiring operations like addition, subtraction, multiplication, and division with decimal alignment.

Working:
To add/subtract decimals, line up the decimal points vertically and add/subtract as whole numbers; to multiply, ignore decimal points, multiply, then count total decimal places in factors and place decimal point; to divide, move decimal point to make divisor a whole number.

Example:
Add $3.25 + 1.7$ .
Solution: Line up decimal points: $3.25 + 1.70 = 4.95$ .

Reason:
Decimals are widely used in real-world measurements, money, and scientific data, and understanding them is essential for translating word problems into algebraic expressions and solving equations with decimal coefficients.

Easy

Medium

Hard

📝 All Decimals in Algebra MCQs

Q1. A student claims that $0.48$ is greater than $0.5$ because $48>5$ . Which reasoning correctly evaluates the claim?

A.The claim is correct because 48 is greater than 5.

B.The claim is incorrect because

0.5=0.50

, and

0.50>0.48

. ✅

C.The claim is correct because decimals are compared using their digits without place value.

D.The claim is incorrect because

0.48=0.50

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: The claim ignores place value. Writing both numbers with the same number of decimal places gives $0.48$ and $0.50$ . Comparing hundredths shows that 48 hundredths is less than 50 hundredths.

Q2. A water tank contains $12.6$ liters. After $3.75$ liters are removed, another $1.8$ liters are added. How much water is in the tank?

7.05

liters

8.85

liters

10.65

liters ✅

16.35

liters

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: First subtract the amount removed: $12.6-3.75=8.85$ . Then add $1.8$ : $8.85+1.8=10.65$ . The problem requires maintaining decimal place values throughout both operations.

Q3. Two students simplify $4.2\times0.35$ . Student A gets $14.7$ , while Student B gets $1.47$ . Which evaluation best explains who is correct?

A.Student A, because multiplying always moves the decimal right.

B.Student A, because

42\times35=1470

C.Student B, because

4.2\times0.35=1.47

, consistent with multiplying by a number less than

1

. ✅

D.Neither, because the product must be greater than

4.2

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: Student B is correct. Since $0.35$ is less than $1$ , multiplying $4.2$ by it should produce a smaller number. Calculating gives $4.2\times0.35=1.47$ , confirming the result.

Q4. A rectangular garden has length $6.4$ m and width $3.25$ m. A path occupies $2.5$ square meters. What area remains for planting?

18.30

square meters ✅

20.80

square meters

23.40

square meters

25.90

square meters

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: The garden's total area is $6.4\times3.25=20.8$ square meters. Subtracting the path area gives $20.8-2.5=18.3$ square meters available for planting.

Q5. A number line marks $0.2,\ 0.35,\ 0.5,$ and $0.65$ at equally spaced positions. Which statement correctly describes the spacing between consecutive marks?

A.Each interval represents

0.10

B.Each interval represents

0.15

. ✅

C.Each interval represents

0.20

D.The intervals are unequal because the decimals have different digits.

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Subtracting consecutive values gives $0.35-0.20=0.15$ , $0.50-0.35=0.15$ , and $0.65-0.50=0.15$ . Therefore every marked interval represents the same distance, $0.15$ .

Q6. A learner calculates $7.5-2.86$ as $5.36$ . Which error most likely caused the result, and what is the correct value?

A.The learner added instead of subtracting; the value is

10.36

B.The learner aligned digits incorrectly; the correct value is

4.64

. ✅

C.The learner ignored the decimal point; the correct value is

4.54

D.The learner borrowed incorrectly; the correct value is

5.64

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The decimal points must be aligned before subtracting. Writing $7.50-2.86$ gives $4.64$ . The incorrect $5.36$ likely results from misaligning place values during subtraction.

Q7. A shop offers two pricing methods for an item originally costing $24.50$ : Method A subtracts $3.75$ , then applies a $10\%$ discount; Method B first applies the $10\%$ discount, then subtracts $3.75$ . Which method gives the lower final price?

A.Method A, giving

18.675

B.Method B, giving

18.30

. ✅

C.Both methods give exactly

18.30

D.Method A, giving

20.75

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: Method A gives $(24.50-3.75)\times0.90=18.675$ . Method B gives $24.50\times0.90-3.75=18.30$ . The fixed subtraction is more valuable when applied after the percentage reduction, so Method B is lower.

🔗 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

←Previous Topic:Evaluate Variable Expressions with Fractions📝 Decimals in AlgebraReading and writing decimals:Next Topic→