Numbers and Counting
English Basic Vocabulary - Part 2 · 50 lessons
What does “Digit Sum” mean?
A is correct: "Digit sum" literally means adding up each individual digit in a number. For example, the digit sum of 234 is 2 + 3 + 4 = 9.
B is wrong: That would be the *product* of digits, not the sum. Multiplying the digits of 234 would give 2 × 3 × 4 = 24, which is a different operation entirely.
What does “Single Digit” mean?
Why A is correct:
A "single digit" means just one digit—any of the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. It's a number you can write with just one symbol.
Why B is wrong:
This contradicts the meaning. "Single" means one, not more than one. A number with more than one digit (like 15 or 342) is called "multi-digit," not single digit.
What does “Double Digit” mean?
Why A is correct:
"Double digit" literally means a number with two digits. Numbers from 10–99 all have exactly two digits, so this is the definition.
Why B is wrong:
Numbers below 10 (like 5) have only one digit, and numbers above 99 (like 100) have three or more digits. Neither of these are "double digit"—they're single digit or triple digit instead.
What does “Triple Digit” mean?
Why A is correct:
"Triple digit" means three digits, which are numbers from 100 to 999. These all have exactly three digits in them.
Why B is wrong:
Numbers below 100 (like 5 or 47) have one or two digits, not three. Numbers above 999 (like 1,000 or 5,280) have four or more digits, not three. So B describes numbers that are *not* triple digits.
What does “Counting Principle” mean?
Correct Answer: A
The Counting Principle (also called the Fundamental Counting Principle) says you multiply the number of choices at each step to find total outcomes. For example, if you choose a shirt (3 ways) and pants (2 ways), you have 3 × 2 = 6 total outfits.
Why B is wrong:
Option B contradicts the principle—it claims there's only *one* way to do something, which makes no sense for a counting tool. The Counting Principle is useful precisely *because* there are multiple independent choices to combine.
What does “Binary Number” mean?
Why A is correct:
Binary literally means "two," and the binary number system uses exactly two symbols (0 and 1) to represent all numbers. This is the foundation of how computers work.
Why B is wrong:
This describes a number system with *more than two* symbols, which is the opposite of binary. For example, our everyday decimal system uses 10 symbols (0–9), making it a multi-symbol system, not binary.
What does “Octal Number” mean?
Why A is correct:
Octal means base-8, so it uses exactly 8 digits: 0, 1, 2, 3, 4, 5, 6, and 7. Any digit 8 or higher doesn't exist in octal.
Why B is wrong:
This contradicts the definition. Octal *only* uses digits 0–7, not anything outside that range. Option B describes systems like hexadecimal (which uses 0–9 and A–F) or decimal (0–9), but not octal.
What does “Hexadecimal Number” mean?
Why A is correct:
Hexadecimal is base-16, meaning it uses 16 different symbols: the digits 0–9 (that's 10 symbols) plus letters A–F (that's 6 more). For example, "FF" in hex equals 255 in decimal. This is the accurate definition.
Why B is wrong:
This option contradicts what hexadecimal actually is. Hexadecimal *requires* letters A–F to represent values 10–15. Without them, you couldn't properly express all numbers in base-16. Option B is simply incorrect.
What does “Place Value” mean?
A is correct. Place value means a digit's worth depends on *where* it sits in a number. For example, the 5 in 50 means five tens (50), but the 5 in 500 means five hundreds (500)—same digit, different value based on position.
B is wrong. This describes the *face value* (or absolute value) of a digit—its value no matter where it appears. A 5 is always worth 5 by itself, but in a number like 537, the 5 is worth 500 because of its position.
What does “Rounding Number” mean?
A is correct: Rounding simplifies a number by adjusting it to a nearby "round" value (like 10, 100, or the nearest whole number), making it easier to work with while staying close to the original number.
B is wrong: Rounding does the opposite—it brings numbers *closer* to a target accuracy level, not away from it. Moving away would make numbers less useful and less precise.
What does “Sequential Order” mean?
A is correct: "Sequential" means following one thing after another in a connected chain. Think of it like steps in a recipe or chapters in a book—each comes in a specific, logical order.
B is wrong: Random or unorganized is the *opposite* of sequential. If something is sequential, it has a clear pattern and order, not chaos.
What does “Ordinal Counting” mean?
Correct Answer: A
Ordinal counting uses numbers to show *position or order* — like "1st place," "2nd in line," or "3rd chapter." The word "ordinal" itself means "order."
Why B is wrong:
Using numbers to show *quantity* (like "I have 5 apples") is called cardinal counting, not ordinal. Cardinal numbers answer "how many," while ordinal numbers answer "which position."
What does “Cardinality” mean?
Correct Answer: A
Cardinality literally means "how many" elements are in a set. For example, the set {apple, banana, orange} has a cardinality of 3.
Why B is wrong:
The arrangement or sequence of elements describes *order*, not cardinality. Cardinality doesn't care whether elements are arranged as {1, 2, 3} or {3, 2, 1}—both have a cardinality of 3 because they contain the same number of items.
What does “Bijection” mean?
Why A is correct:
A bijection requires two properties: injective (one-to-one—no two different inputs map to the same output) and surjective (onto—every element in the target set gets mapped to). Together, these create a perfect pairing where each input gets exactly one unique output, and nothing in the target set is left unmapped.
Why B is wrong:
This describes the *opposite* of a bijection. Saying a bijection is "neither injective nor surjective" directly contradicts the definition—a bijection must be *both* of these properties.
What does “Parity” mean?
A is correct. Parity specifically refers to whether a number is even or odd—this is a fundamental concept in number theory. An integer's parity determines its divisibility by 2.
B is wrong. Whether a number is positive or negative describes its *sign*, not its parity. A number can be both even and negative (like –4) or odd and negative (like –7).
What does “Integral Part” mean?
A is correct. The "integral part" refers to the whole number portion of a number—for example, the integral part of 7.3 is 7. The word "integral" comes from "integer," meaning whole number.
B is wrong. This describes the *fractional* part (or decimal part), which is the opposite of what "integral" means. In 7.3, the fractional part is 0.3.
What does “Fractional Part” mean?
Correct Answer (A):
The fractional part is everything after the decimal point because it represents pieces smaller than a whole number. For example, in 3.75, the fractional part is .75 (seventy-five hundredths).
Why B is wrong:
The part before the decimal point is called the "whole number part" or "integer part"—it represents complete units, not fractions.
What does “Cumulative Count” mean?
A is correct: Cumulative means "growing by adding together," so cumulative count is a running total that keeps getting larger as you add each new number. For example: 2, 5, 9, 15 shows cumulative counts (2, then 2+3=5, then 5+4=9, etc.).
B is wrong: This describes an individual or separate count for each item, not cumulative. That's the opposite of cumulative—there's no "adding up" happening across the sequence.
What does “Perfect Number” mean?
Why A is correct:
A perfect number equals the sum of its proper divisors (all divisors except itself). For example, 6 is perfect because its divisors are 1, 2, and 3, and 1 + 2 + 3 = 6. This is the mathematical definition.
Why B is wrong:
This is the opposite of the definition—it describes numbers that are *not* perfect. Following this would exclude actual perfect numbers like 6, 28, and 496.
What does “Abundant Number” mean?
Correct Answer (A):
An abundant number is one where the sum of its proper divisors (all divisors except the number itself) exceeds the number. For example, 12 has proper divisors 1, 2, 3, 4, 6, which sum to 16—more than 12, making it abundant.
Why B is wrong:
This describes a *deficient* number, where proper divisors sum to less than the number itself. For example, 8 has proper divisors 1, 2, 4 summing to only 7.
What does “Deficient Number” mean?
Correct answer: A
A deficient number is one where the number itself is greater than the sum of its proper divisors (all divisors except the number itself). For example, 8 has proper divisors 1, 2, 4, which sum to 7—and 8 > 7, so 8 is deficient.
Why B is wrong:
Option B describes a abundant number instead. When a number is less than the sum of its proper divisors, it's called abundant (like 12, whose proper divisors 1, 2, 3, 4, 6 sum to 16).
What does “Pentadecimal Number” mean?
Why A is correct:
"Penta-" means 5 and "-decimal" refers to 10, so pentadecimal = 5 + 10 = base 15. In this number system, you use digits 0–9 and symbols for 10–14 (like A, B, C, D, E).
Why B is wrong:
Base 16 is called hexadecimal (hex = 6, so 6 + 10 = 16). That's a different system entirely.
What does “Duo-Decimal Number” mean?
A is correct. "Duo" means two and "decimal" refers to ten, so "duo-decimal" literally means "two-ten" or 12. This is a base-12 number system, also called duodecimal or dozenal.
B is wrong. A base-10 system is called decimal (just "decimal," not "duo-decimal"). Base 10 has no "duo" prefix, so this misses the meaning of the word.
What does “Tally Marks” mean?
Why A is correct:
Tally marks are literally simple lines (usually grouped in fives with a diagonal line through four) used to record counts. This is their actual purpose—a quick, visual way to keep track of quantities.
Why B is wrong:
This directly contradicts what tally marks are. They exist specifically *for* counting and tracking numbers, so saying they don't is false.
What does “Addend” mean?
Correct (A): An addend is literally a number you're adding. In the problem 3 + 5 = 8, both 3 and 5 are addends. The word comes from "add," so it must involve addition.
Wrong (B): That describes a *subtrahend* (the number being subtracted), not an addend. Since addend is rooted in addition, not subtraction, this is incorrect.
What does “Minuend” mean?
Correct Answer: A
In subtraction, the minuend is the starting number that you subtract from. For example, in 10 − 3 = 7, the 10 is the minuend. The word comes from Latin meaning "to diminish"—it's the number that gets diminished.
Why B is wrong:
Option B describes addition, not subtraction. The number you add to is called an addend, not a minuend. Minuend is specific to subtraction problems.
What does “Subtrahend” mean?
Correct Answer (A):
"Subtrahend" comes from the word "subtract," so it refers to the number being taken away. In the problem 10 – 3 = 7, the subtrahend is 3 (the number you subtract).
Why B is wrong:
That describes addition, not subtraction. A number being added is called an "addend," not a subtrahend.
What does “Greatest Common Divisor” mean?
Why A is correct:
The GCD is the *largest* number that goes evenly into a set of numbers with no remainder. For example, 12 and 18 share divisors 1, 2, 3, and 6—and 6 is the greatest one.
Why B is wrong:
This describes the Least Common Multiple (LCM), not the GCD. The LCM is the *smallest* number that two or more numbers divide into evenly. Also, B uses "multiplies into" which is backwards—we need numbers that *divide into* our original numbers, not the other way around.
What does “Least Common Multiple” mean?
A is correct. The LCM is the smallest number that all your given numbers divide into evenly with no remainder. For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 divide into exactly.
B is wrong. This describes the Greatest Common *Divisor* (GCD), not the LCM. The GCD is the largest number that divides *into* your numbers, which is the opposite of what we're looking for.
What does “Quadratic Equation” mean?
Why A is correct:
"Quadratic" comes from "quad," meaning four, but refers to the *square* (power of 2)—like a four-sided square shape. A quadratic equation has its highest power as 2, like x² + 3x + 2 = 0.
Why B is wrong:
An equation where the highest power is a cube (power of 3) is called a *cubic* equation, not quadratic. That's a different type.
What does “Permutation” mean?
A is correct. A permutation is specifically about *order*—it counts different arrangements as different results. For example, ABC and BAC are two different permutations because the sequence matters.
B is wrong. This describes a combination, not a permutation. Combinations ignore order, so {A, B, C} and {B, A, C} would be the same combination. The word "arranging" in option A is the key clue that order matters.
What does “Numerical Order” mean?
Correct Answer (A): Numerical order means organizing items based on their numeric values—like arranging 3, 7, 1, 9 into 1, 3, 7, 9. It's a systematic, rule-based arrangement where numbers determine the sequence.
Why B is wrong: Random arrangement is the opposite of numerical order. If you ignore the numbers entirely, you're not putting things in numerical order—you're doing the exact opposite.
What does “Sequential Numbering” mean?
Correct Answer (A): "Sequential" means following in order, one after another. So sequential numbering is assigning numbers in continuous order—like 1, 2, 3, 4—where each number logically follows the previous one.
Why B is wrong: This option contradicts the meaning of "sequential." If numbers don't follow one another in order (like 1, 5, 3, 9), that would be *random* or *non-sequential* numbering, not sequential numbering.
What does “Double-Figure Digit” mean?
Correct Answer: A
A "double-figure digit" means a number with two digits, like 10, 25, or 99. The word "double" means two, and "figure" is another word for digit or numeral. So it's simply a two-digit number.
Why B is wrong:
A number with three figures or numerals would be called a "three-figure number" (like 100–999), not a "double-figure" number. The prefix "double" specifically means two, not three.
What does “Triple-Figure Digit” mean?
Correct Answer: A
"Triple-Figure Digit" means a number with three digits (like 100–999). "Triple" means three, and the term refers to how many figures or numerals make up the number.
Why B is wrong:
Two figures make a two-digit number (10–99), which would be called a "double-figure digit," not triple. The prefix "triple" specifically indicates three, not two.
What does “Incremental Counting” mean?
Correct answer (A): "Incremental" means to increase or add in small steps. So incremental counting means you start at a number and keep adding 1 each time (1, 2, 3, 4...). This is the standard way most people learn to count.
Why B is wrong: That describes *decreasing* by one, which would be called "decremental" or "counting backward" (5, 4, 3, 2...). The word "increment" specifically means to go up, not down.
What does “Decrease Count” mean?
Correct Answer (A): "Decrease" means to reduce or make smaller, so "Decrease Count" literally means to reduce a number by one each time—like counting backward (10, 9, 8...).
Why B is wrong: That describes "Increase Count," which is the opposite. Increasing means making bigger, not smaller.
What does “Unary Number” mean?
Correct Answer (A): "Unary" means "one," so a unary number system uses only a single symbol (typically 1 or a tally mark) repeated to show quantity. For example, the number 5 would be written as 11111. It's the simplest possible counting system.
Why B is wrong: That describes a standard positional numeral system like decimal or binary, which use *multiple different digits*. Unary is the opposite—it relies on repetition of just one symbol, not variety of digits.
What does “Number Sequence” mean?
A is correct because sequences are fundamentally about *order* and *pattern*—each number follows a specific rule based on its position or the previous number (like 2, 4, 6, 8 or 1, 1, 2, 3, 5 in the Fibonacci sequence).
B is wrong because it describes random, unordered numbers with no pattern—that's not a sequence at all. Sequences must have rules and structure, otherwise we couldn't predict or understand them.
What does “Isolated Digit” mean?
Why A is correct:
"Isolated" means separated or alone. An isolated digit literally stands by itself, not part of any larger group or pattern.
Why B is wrong:
This describes the *opposite* of isolated. A digit included in a group or sequence is connected to other digits, not isolated.
What does “Fractional Sequencing” mean?
Correct Answer (A):
"Fractional" literally means "involving fractions," so fractional sequencing is a sequence where the numbers progress as fractions (like 1/2, 1/4, 1/8 or 1/3, 2/3, 1). The term directly describes what type of numbers are being sequenced.
Why B is wrong:
If the sequence involved only whole numbers (1, 2, 3, 4...), it would be called "whole number sequencing" or just a "number sequence"—not fractional sequencing. The word "fractional" would have no meaning in that context.
What does “Decimal Fraction” mean?
Why A is correct:
A decimal fraction has a denominator that's always a power of 10 (10, 100, 1000, etc.), and we write it using a decimal point instead of showing the fraction bar. For example, 0.5 = 5/10 and 0.25 = 25/100. The digits after the decimal point represent the numerator.
Why B is wrong:
A whole number like 7 isn't a fraction at all—it has no fractional part. It also has no denominator of 10, so it doesn't fit the definition of a decimal fraction.
What does “Cube Number” mean?
Why A is correct:
A cube number is formed when you multiply an integer by itself twice more (three times total). For example, 2 × 2 × 2 = 8, so 8 is a cube number. We write this as 2³.
Why B is wrong:
This describes the opposite of what a cube number is. Option B describes numbers that *cannot* be expressed as a repeated multiplication, which is incorrect—cube numbers are specifically defined by this multiplication pattern.
What does “Countability” mean?
A is correct: A countable set is one you can match up with natural numbers (1, 2, 3, ...). This includes finite sets and infinite sets like integers or rationals—even though they're infinite, they can be listed in order, making them "countably infinite."
B is wrong: This describes an *uncountable* set, like the real numbers. Uncountable sets are so densely packed that you *cannot* create a one-to-one matching with natural numbers, no matter how you try.
What does “Pell's Sequence” mean?
Correct Answer (A): Pell's Sequence is a real mathematical concept—a specific integer sequence where each term is calculated using a recursive formula (each number depends on previous ones). It's named after John Pell, a 17th-century mathematician. The sequence goes 0, 1, 2, 5, 12, 29... where each term equals 2 times the previous term plus the one before that.
Why B is wrong: Option B describes a *random* or *chaotic* sequence with no pattern. Pell's Sequence is the opposite—it has a very clear, predictable recursive rule that generates each term precisely.
What does “Repeated Subtraction” mean?
Why A is correct:
Repeated subtraction literally means taking away the same amount over and over. For example, 12 − 3 − 3 − 3 − 3 = 0 is repeated subtraction of 3. This is actually how division works: you're seeing how many times you can subtract 3 from 12.
Why B is wrong:
Adding multiple times is the opposite operation—that's called "repeated addition," not repeated subtraction. If you're adding, you're not subtracting.
What does “Number Line” mean?
Why A is correct:
A number line is a visual tool where each point has a specific real number value. It helps us visualize and compare numbers by placing them in order on a line.
Why B is wrong:
This contradicts the entire purpose of a number line. The whole idea is to *assign* numbers to points so we can see numerical relationships spatially. Without numbers, it's just a blank line with no mathematical meaning.
What does “Surd” mean?
A is correct. A surd is specifically a root (like √2 or ∛5) that cannot be simplified to a rational number—it's irrational and goes on forever without repeating as a decimal.
B is wrong. This describes a rational number, which is the opposite of a surd. Rational numbers *can* be written as fractions (like 1/2 or 3/4), while surds cannot.
What does “Mathematical Constant” mean?
Why A is correct:
A mathematical constant is a fixed value that stays the same—like π (pi) or e. It doesn't change no matter how many times you use it or what problem you're solving.
Why B is wrong:
This describes a variable, not a constant. Variables (like x or y) are meant to change and take different values in equations and operations. Constants do the opposite—they're always the same.
What does “Decimal Separator” mean?
Correct Answer (A):
The decimal separator (like a period in 3.14 or a comma in 3,14) *separates* the whole number part from the decimal part. "Separate" means to divide or keep apart, which is exactly what it does—it marks the boundary between these two parts.
Why B is wrong:
"Join" means to connect or bring together, but the decimal separator doesn't join the parts—it divides them. Using "join" reverses the actual function of this symbol.
Practise any of these free
Make an account in under a minute, or try it as a guest first.
Start learning free