Numbers and Counting

Correct answer (A): Numerical order means arranging items according to mathematical or logical rules—like smallest to largest, alphabetically, or by a consistent pattern. This creates a predictable, organized sequence.

Why B is wrong: Random or arbitrary order is the *opposite* of numerical order. If items are scattered without a system, there's no "order" at all—that's chaos, not organization.

Correct answer (A): An integer is a whole number with no fractional or decimal parts. Examples are -3, 0, 5, and 100. This is the mathematical definition.

Why B is wrong: This describes a fraction or rational number (like 1/2 or 0.75), which is the *opposite* of an integer. Integers specifically exclude parts of a whole.

Option A is correct because it accurately defines a decimal: a fraction where the denominator is a power of 10, and the numerator is shown as digits to the right of the decimal point. For example, 0.5 = 5/10 and 0.25 = 25/100.

Option B is wrong because it describes a whole number or integer, which is the opposite of a decimal—decimals specifically represent fractional parts, not complete whole numbers.

Correct Answer (A): Kuantitas numerik yang bukan angka utuh
- A fraction represents a part of a whole, like 1/2 or 3/4—not a complete number.
- It shows how many equal parts you have out of a total number of parts.

Why B is wrong:
- An integer (angka utuh) is a whole number like 1, 2, or 5.
- Fractions are specifically *not* whole numbers—they represent parts of wholes.

Correct Answer (A): Zero represents the absence of quantity—it means "nothing" or "no amount." It's the number that shows when there's a null/empty state.

Why B is wrong: Option B says zero shows "quantity or existence," which is backwards. Zero actually means the *opposite*—the absence or non-existence of something. Numbers like 1, 2, 3 show quantity; zero shows none.

Correct answer (A): A digit is any single numeric symbol from 0 to 9. These 10 symbols are the building blocks we use to write all numbers—for example, the number 25 has two digits: 2 and 5.

Why B is wrong: Letters (A–Z) are called alphabetic characters or letters, not digits. While we might use letters in some contexts (like hexadecimal), the standard meaning of "digit" refers only to the numeric symbols 0–9.

Correct Answer: A (Bilangan bulat yang bukan kelipatan dua)

An odd number is any whole number that cannot be divided evenly by 2—there's always a remainder of 1. Examples: 1, 3, 5, 7, 9. This is exactly what option A says.

Why B is wrong:
Option B describes the opposite—numbers that ARE multiples of 2 are called *even* numbers (2, 4, 6, 8, etc.), not odd numbers.

Correct Answer (A): An even number is any whole number that can be divided evenly by 2 with no remainder. Examples: 2, 4, 6, 8, 10. These are all multiples of 2.

Why B is wrong: This describes *odd* numbers (whole numbers that are NOT multiples of 2), like 1, 3, 5, 7—these leave a remainder when divided by 2.

Correct Answer (A): A prime number has exactly two factors—1 and itself. Examples: 2, 3, 5, 7, 11. This is the mathematical definition.

Why B is wrong: It describes the opposite of a prime number. Numbers with *many* positive divisors are called composite numbers (like 12, which has divisors 1, 2, 3, 4, 6, 12). Prime numbers have the *fewest* divisors possible.

Correct Answer: A. Sebuah bilangan real yang kurang dari nol.

• A negative number is literally any real number smaller than zero—like -5, -0.3, or -100. These appear to the left of zero on a number line.

• Why B is wrong: That describes a *positive* number (greater than zero), which is the opposite of negative.

Correct Answer (A): "A real number greater than zero"
This is the definition of a positive number—any value on the number line to the right of zero, like 1, 2.5, or 100.

Why B is wrong:
"A real number less than zero" describes a *negative* number (like -5 or -0.3), not a positive number. These are opposites.

Correct answer (A): A whole number is any non-negative integer (0, 1, 2, 3, ...). It has no fractional or decimal part, and includes zero and all positive integers.

Why B is wrong:
- Says "specific fraction" — whole numbers are NOT fractions
- Says "negative" — whole numbers start at 0 and go up (no negatives)
- Contradicts the definition entirely

Correct Answer (A): Natural numbers are the counting numbers we use daily: 1, 2, 3, 4... Most definitions include 0 as well, making the set {0, 1, 2, 3...}. These are all positive whole numbers.

Why B is wrong: Natural numbers are NOT negative. Negative numbers like -1, -2, -3 are integers, but not natural numbers. Option B incorrectly describes negative integers instead.

Option A (Correct): This correctly defines a composite number—a positive integer that has at least one positive divisor other than 1 or itself. For example, 6 is composite because it's divisible by 2 and 3, not just 1 and 6.

Option B (Wrong): This describes negative integers, but composite numbers are defined only for positive integers. Also, the phrase "no divisors except 1 or itself" describes *prime* numbers, not composite numbers—the opposite of what we're looking for.

Option A is correct because real numbers include all values that form a continuous line—integers, decimals, fractions, and irrational numbers like π. You can place any real number on a number line to represent a distance.

Option B is wrong because:
- Real numbers are continuous, not discrete (discrete means separate, countable values)
- Real numbers can represent distances on a line, which is their key characteristic
- This description actually fits integers or natural numbers better, which are discrete sets

Correct Answer (A):
An imaginary number is specifically a complex number that contains the imaginary unit *i* (where i² = −1). It's written as a real number multiplied by *i*, like 3*i* or 5*i*. These numbers don't exist on the regular number line but are useful in mathematics and engineering.

Why B is wrong:
Option B contradicts itself—it says imaginary numbers are "real numbers that can't be written with *i*," but that's the opposite of what imaginary numbers are. Real numbers are things like 2, −5, or 3.14; they don't involve *i* at all. Imaginary numbers must have *i* in them.

Correct Answer (A): A rational number is defined as any number that can be expressed as a fraction or quotient of two integers (like 3/4, -2, or 0.5). This is the actual mathematical definition.

Why B is wrong: This describes an *irrational* number instead—numbers that cannot be written as a simple fraction, like π or √2. It's the opposite of what rational means.

Correct Answer (A): An irrational number is one that *cannot* be expressed as a ratio of two integers. Examples include π, √2, and e—they have infinite, non-repeating decimals.

Why B is wrong: That's the definition of a *rational* number, not irrational. Rational numbers like 1/2 or 3/4 can be written as ratios of two integers.

Correct Answer (A): "Sejauh mana sebuah angka berbeda dari nol" (How far a number is from zero)

• This is correct because absolute value measures the *distance* of any number from zero on a number line—always positive, regardless of direction. For example, |−5| = 5 and |5| = 5 because both are 5 units away from zero.

Why B is wrong:

• "Berassociasi dengan nol" (associated with zero) is too vague and doesn't capture the specific meaning. Absolute value isn't about association—it's about measurable distance.

Correct Answer (A): Counting numbers are the numbers we use to count objects—1, 2, 3, 4, and so on. They start at 1 and go infinitely upward, and their whole purpose is to tell us "how many" of something we have.

Why B is wrong: This is the opposite of what counting numbers are. Counting numbers ARE used for counting, not the other way around. Numbers like 0 or negative numbers aren't counting numbers because we don't use them to count physical objects.

Correct Answer (A): Numerical value means the size/magnitude of a number *without* considering its sign. This is the definition of absolute value—both -5 and +5 have the same numerical value of 5.

Why B is wrong: Option B says "considering the sign," which is incorrect. If we consider the sign, -5 and +5 would be different, but numerical value treats them as equal in magnitude.

A is correct: "Sum" means the result when you add two or more numbers together. For example, the sum of 3 + 5 is 8.

B is wrong: That describes subtraction (taking one number away from another), not a sum. Subtraction gives you a *difference*, not a sum.

Correct Answer (A): Hasil ketika satu angka dikurangi dari angka lain.
"Difference" specifically means the result of *subtraction*—when you take one number away from another. For example, the difference between 10 and 3 is 7 (because 10 − 3 = 7).

Why B is wrong:
Option B describes *addition* (adding one number to another), not difference. That result is called a "sum," not a difference.

A is correct: "Product" means the result when you multiply two or more numbers together. For example, 3 × 4 = 12, where 12 is the product.

B is wrong: This describes division, not multiplication. When you divide one number by another, the result is called a "quotient," not a product.

Correct Answer (A): Hasil pembagian satu angka oleh yang lain.

A quotient is the answer you get when you divide one number by another. For example, when you divide 10 by 2, the quotient is 5.

Why B is wrong:

Option B describes a "product," not a quotient. A product is the result of *multiplying* numbers together, not dividing them. For example, 3 × 4 = 12 (the product is 12).

Correct Answer (A):
An exponent tells you how many times to multiply a number by itself. For example, 2³ means 2 × 2 × 2 = 8.

Why B is wrong:
Exponents are about repeated multiplication, not division. If you divided repeatedly, you'd get smaller and smaller numbers, which isn't what exponents do.

Correct Answer (A): A square root is a number that, when multiplied by itself, gives you the original number. For example, the square root of 9 is 3, because 3 × 3 = 9.

Why B is wrong: If you divide a number by itself, you always get 1 (like 9 ÷ 9 = 1), not the original number. That's division, not finding a square root.

Correct Answer (A): This is right because "percentage" literally means "per cent" (per 100). It expresses a part of a whole by dividing it into 100 equal parts. For example, 25% means 25 out of 100 parts.

Why B is wrong: Option B says the whole is *multiplied* by 100, which is backwards. Multiplying by 100 would give you a much larger number, not a percentage. Percentages work by *dividing* into 100 parts, not multiplying by it.

Correct Answer (A): Produk semua bilangan bulat positif hingga suatu bilangan
- Factorial means you *multiply* all positive integers up to a number. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

Why B is wrong:
- Option B says "jumlah" (sum), which means adding numbers together. Factorial uses multiplication, not addition. If you added 5 + 4 + 3 + 2 + 1 = 15, that's not a factorial.

Correct Answer (A): "A number to be divided by another number"
In division, the dividend is the number you're dividing up. For example, in 12 ÷ 3, the 12 is the dividend (what you're dividing), and 3 is the divisor (what you're dividing by).

Why B is wrong:
Multiplication uses different terms—the numbers being multiplied are called "factors," not dividends. The word "dividend" specifically refers to division operations.

Correct Answer (A): A divisor is the number you divide *by*. In the division problem 12 ÷ 3 = 4, the divisor is 3 because it's the number doing the dividing.

Why B is wrong: Multiplying is the opposite operation from division. The number you multiply *by* is called a multiplier or factor, not a divisor.

Correct Answer (A): This definition is right because "multiple" means more than one—it describes things that have many parts, pieces, or elements together. Examples: multiple choice (many choices), multiple colors (several colors), multiple people (many people).

Why B is wrong: This option describes the opposite meaning. It talks about being "singular or isolated," which is what "single" or "solitary" means—not "multiple." Multiple means the opposite: many, not one.

Correct Answer (A): This is the definition of subtraction—it describes taking away or removing a quantity from another quantity. "Pengurangan" literally means "reduction" or "subtraction" in Indonesian, which directly matches what the mathematical operation does.

Why B is wrong: Option B describes *addition* (menambahkan = adding), not subtraction. Addition combines quantities together, while subtraction removes one quantity from another—the opposite process.

Correct Answer: A

"Addition" means the action or process of adding or combining things together. When you add numbers or objects, you're putting them together to make a larger amount.

Why B is wrong:
Option B describes subtraction (removing or reducing), which is the opposite of addition. Subtraction makes amounts smaller, while addition makes them larger.

Correct Answer (A): "Greater than" means something is larger or higher in amount/degree. When we say 5 is greater than 3, we mean 5 is bigger. This is the actual definition of the phrase.

Why B is wrong: This describes the opposite meaning—it defines "less than" instead. Option B talks about being smaller or lower, which is the reverse of what "greater than" means.

Correct Answer (A): Menjadi derajat atau kuantitas yang lebih kecil atau lebih tinggi.

"Less than" means something is smaller or lower in amount, degree, or value. For example, 5 is less than 10 because 5 is a smaller number.

Why B is wrong:
Option B says "greater or higher," which is the opposite meaning. That would describe "more than" or "greater than," not "less than."

Correct Answer (A): "Equal To" means having the same capability, quantity, effect, size, etc. as something else. That's the definition of equality—two things being identical or the same in some measurable way.

Why B is wrong: It says "different from" (berbeda), which is the opposite of equal. If things are different, they are NOT equal to each other.

Correct answer (A): "Infinity" means the quality or state of being unlimited or endless. This is the direct definition—infinity describes something with no bounds, limits, or end point.

Why B is wrong: Option B says the opposite—it defines infinity as being *limited* or *restricted*. This contradicts what infinity actually means. Infinity is the complete opposite of having limits.

Correct Answer (A): This is right because a factor is any number that divides evenly into another number with no remainder. For example, 3 and 4 are factors of 12 because 12 ÷ 3 = 4 and 12 ÷ 4 = 3 (both divide evenly).

Why B is wrong: Option B describes a multiplier or one of the numbers being multiplied together, but it's too vague and incomplete. A factor is specifically a number that divides *into* another number evenly, not just "a number that multiplies with another." The key difference is about division and finding what divides evenly, not just multiplication.

Correct Answer (A): This is the definition of multiplication—it describes the action or process of multiplying or the state of being multiplied. This matches what multiplication actually means in mathematics.

Why B is wrong: This option describes *subtraction* (the action of reducing or subtracting), not multiplication. Subtraction removes amounts, while multiplication combines or repeats amounts.

Correct Answer (A): "A number that when multiplied by itself three times equals the original number"

• This is the definition of cube root. For example, the cube root of 8 is 2, because 2 × 2 × 2 = 8.

Why B is wrong:
- Option B describes an *inverse relationship* with cubes, which is not what cube root means. Cube root is the *opposite operation* of cubing (finding the base number), not an inverse proportion.

Why A is correct:
A base number is a foundational reference number used across multiple mathematical systems—it's the core concept in number systems (like base 10, binary base 2) and in logarithms (where you have different bases). This broad applicability makes it the accurate definition.

Why B is wrong:
B incorrectly limits "base number" to *only* geometry operations. While "base" does appear in geometry (the bottom side of a shape), the term "base number" specifically refers to a mathematical reference value used in various systems, not just geometry.

Why A is correct:
Integer division means dividing two numbers and keeping only the whole number result, throwing away any remainder. For example, 7 ÷ 2 = 3 (not 3.5), because we discard the 0.5 remainder.

Why B is wrong:
This describes regular division where you keep the decimal or fraction. That's not integer division—integer division specifically *ignores* the remainder, not includes it.

Correct Answer (A):
Decimal places are the digits *after* the decimal point. They represent fractional parts (tenths, hundredths, thousandths, etc.). For example, in 3.456, there are three decimal places: 4, 5, and 6.

Why B is wrong:
Digits to the *left* of the decimal point are called "whole number places" or positions in the ones, tens, hundreds, etc. These are not decimal places—they're part of the whole number portion.

Why A is correct:
Ordinal numbers describe *position or order* in a sequence—1st, 2nd, 3rd, etc. They tell you where something ranks or comes in a line.

Why B is wrong:
This describes *cardinal numbers* (1, 2, 3, etc.), which count *quantities* or "how many" items exist in a group. Cardinal numbers answer "how many?", while ordinal numbers answer "what position?"

A is correct. Cardinal numbers tell you *how many* things there are—they measure quantity. Examples like "one, two, three" show amounts (1 apple, 2 books, 3 cars).

B is wrong because that describes *ordinal* numbers, which show position or order in a sequence (1st, 2nd, 3rd, first, second, third).

Correct Answer (A):
An arithmetic sequence has a constant difference between consecutive terms. For example: 2, 5, 8, 11... (difference of +3 each time). You add the same number repeatedly.

Why B is wrong:
Option B describes a geometric sequence, not arithmetic. A geometric sequence has a constant *ratio* (multiplying by the same number), like 2, 6, 18, 54... (multiplying by 3 each time). That's different from arithmetic.

Option A is correct because a geometric sequence is defined by a *constant ratio* between consecutive terms. For example: 2, 6, 18, 54 (each term multiplied by 3).

Option B is wrong because it describes an *arithmetic sequence*, where you add/subtract a constant difference between terms instead. For example: 2, 5, 8, 11 (each term adds 3).

The key difference: geometric uses multiplication (ratio), arithmetic uses addition (difference).

Why A is correct:
The "unit digit" (or ones place) is the rightmost digit in any number. It represents the "ones" in the place value system. For example, in 347, the unit digit is 7.

Why B is wrong:
The leftmost digit is called the "leading digit" or "most significant digit," not the unit digit. In 347, the leftmost digit (3) is in the hundreds place, not the ones place.

Correct Answer (A):
Decimal expansion means writing any fraction or real number using the decimal (base-10) system—the everyday number system we use. For example, 1/2 = 0.5 or π ≈ 3.14159...

Why B is wrong:
Binary is base-2 (using only 0s and 1s), not the decimal system. That would be called "binary expansion," not decimal expansion.