Math trivia
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The document discusses two methods for determining prime numbers: the Sieve of Eratosthenes and the Sieve of Atkin. The Sieve of Eratosthenes involves listing all numbers from 1 to 100, crossing out numbers that are not prime like multiples of 2 and 3, and the remaining numbers are prime. The Sieve of Atkin is a newer and faster method that is based on the Sieve of Eratosthenes but used in algorithms due to being tedious to do by hand.
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Rounding to a Whole Number
To round a decimal number to the nearest whole number, look at the digit in the tenths column. If the tenths digit is 0-4, round down. If it is 5-9, round up. However, if rounding up results in the units digit becoming a 9 (e.g. 9.57), round up to the next multiple of ten instead of just the units place (e.g. rounding 9.57 up to 10 instead of 9).
3.4 rounding decimals
The document discusses rounding decimals to a given place value by looking at the digit in the place to the right. If the digit is 4 or less, round down. If the digit is 5 or greater, round up. Examples are provided of rounding decimals to the hundredths, tenths and ones place. The document also discusses rounding very small numbers to the place value of the leading digit, which is the first non-zero digit reading from left to right. Examples of rounding decimals to the leading digit are given.
Irrational numbers
This document discusses rational and irrational numbers. It defines rational numbers as numbers that can be written as fractions, and irrational numbers as numbers that cannot be written as fractions, because they are either non-terminating decimals or decimals that do not repeat. The square roots of perfect squares are rational, while the square roots of numbers that are not perfect squares are irrational. Some examples of rational and irrational numbers are provided.
Rounding Decimal Numbers
Here are the steps to round each number as indicated in Exercise 3.2 on pages 105 and 106:
a. 4.231 to 2 decimal places is 4.23
b. 0.75 to 1 decimal place is 0.8
c. 2.076 to 2 decimal places is 2.08
d. 0.698 to 2 decimal places is 0.70
e. 23.357 to 1 decimal place is 23.4
f. 48.6929 to 3 decimal places is 48.693
g. 639.678 to the nearest hundred is 640
h. 12.364 to the nearest ten is 12.4
i. 95.89 to the nearest ten is 100
j.
Rounding off numbers
This document explains how to round numbers to the nearest ten, hundred, and thousand. For rounding to the nearest ten, examine the ones place digit and compare it to 5; if less than 5, replace the ones place with 0 and leave the tens place unchanged, if greater than or equal to 5, replace the ones place with 0 and add 1 to the tens place. The same process is followed for rounding to the nearest hundred and thousand, examining the tens place and hundreds place respectively and adjusting that place value or the place to its left based on the comparison to 5. Examples are provided to illustrate rounding 54 to 50, 65 to 70, and 56 to 60 when rounding to the nearest ten.
Round Decimals
This document provides instructions for rounding decimals to different places. It explains that rounding decimals works similarly to rounding whole numbers, with the only difference being the presence of a decimal point. The key rules covered are: 1) look at the digit to the right of where you are rounding; 2) if the digit is 4 or less, round down; 3) if the digit is 5 or more, round up. Several examples are provided to demonstrate how to apply these rules when rounding decimals to the nearest tenth or hundredth.
Whole numbers
The document defines and provides examples of whole numbers, natural numbers, predecessors, successors, and the number line. It explains how addition, subtraction, and multiplication can be represented on the number line. Properties of whole numbers are discussed, including closure, commutativity, associativity, and the distributive property. Examples are given for each property to illustrate how operations with whole numbers follow consistent rules and patterns.
3.4 rounding decimals
This document provides instructions on rounding decimals to a specified place value. It explains that when rounding, if the digit to the right of the specified place value is 4 or less, round down, and if it is 5 or greater, round up. Examples are provided rounding decimals to the nearest tenth, hundredth, and thousandth using number lines. Practice problems are also included for students to round decimals on their own.
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Rounding to a Whole Number
To round a decimal number to the nearest whole number, look at the digit in the tenths column. If the tenths digit is 0-4, round down. If it is 5-9, round up. However, if rounding up results in the units digit becoming a 9 (e.g. 9.57), round up to the next multiple of ten instead of just the units place (e.g. rounding 9.57 up to 10 instead of 9).
3.4 rounding decimals
The document discusses rounding decimals to a given place value by looking at the digit in the place to the right. If the digit is 4 or less, round down. If the digit is 5 or greater, round up. Examples are provided of rounding decimals to the hundredths, tenths and ones place. The document also discusses rounding very small numbers to the place value of the leading digit, which is the first non-zero digit reading from left to right. Examples of rounding decimals to the leading digit are given.
Irrational numbers
This document discusses rational and irrational numbers. It defines rational numbers as numbers that can be written as fractions, and irrational numbers as numbers that cannot be written as fractions, because they are either non-terminating decimals or decimals that do not repeat. The square roots of perfect squares are rational, while the square roots of numbers that are not perfect squares are irrational. Some examples of rational and irrational numbers are provided.
Rounding Decimal Numbers
Here are the steps to round each number as indicated in Exercise 3.2 on pages 105 and 106:
a. 4.231 to 2 decimal places is 4.23
b. 0.75 to 1 decimal place is 0.8
c. 2.076 to 2 decimal places is 2.08
d. 0.698 to 2 decimal places is 0.70
e. 23.357 to 1 decimal place is 23.4
f. 48.6929 to 3 decimal places is 48.693
g. 639.678 to the nearest hundred is 640
h. 12.364 to the nearest ten is 12.4
i. 95.89 to the nearest ten is 100
j.
Rounding off numbers
This document explains how to round numbers to the nearest ten, hundred, and thousand. For rounding to the nearest ten, examine the ones place digit and compare it to 5; if less than 5, replace the ones place with 0 and leave the tens place unchanged, if greater than or equal to 5, replace the ones place with 0 and add 1 to the tens place. The same process is followed for rounding to the nearest hundred and thousand, examining the tens place and hundreds place respectively and adjusting that place value or the place to its left based on the comparison to 5. Examples are provided to illustrate rounding 54 to 50, 65 to 70, and 56 to 60 when rounding to the nearest ten.
Round Decimals
This document provides instructions for rounding decimals to different places. It explains that rounding decimals works similarly to rounding whole numbers, with the only difference being the presence of a decimal point. The key rules covered are: 1) look at the digit to the right of where you are rounding; 2) if the digit is 4 or less, round down; 3) if the digit is 5 or more, round up. Several examples are provided to demonstrate how to apply these rules when rounding decimals to the nearest tenth or hundredth.
Whole numbers
The document defines and provides examples of whole numbers, natural numbers, predecessors, successors, and the number line. It explains how addition, subtraction, and multiplication can be represented on the number line. Properties of whole numbers are discussed, including closure, commutativity, associativity, and the distributive property. Examples are given for each property to illustrate how operations with whole numbers follow consistent rules and patterns.
3.4 rounding decimals
This document provides instructions on rounding decimals to a specified place value. It explains that when rounding, if the digit to the right of the specified place value is 4 or less, round down, and if it is 5 or greater, round up. Examples are provided rounding decimals to the nearest tenth, hundredth, and thousandth using number lines. Practice problems are also included for students to round decimals on their own.
Whole numbers
The document discusses whole numbers and natural numbers. It defines natural numbers as counting numbers and notes that natural numbers along with zero form the set of whole numbers. It provides examples of finding predecessors and successors of numbers and using the number line to demonstrate addition, subtraction and multiplication of whole numbers. It poses questions about properties of natural numbers and whole numbers.
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This document describes how to create stemplots, which are a visual way to represent data values. It involves ordering the data from least to greatest, using all but the last digit of each number as "stems" on the left side of a T-chart, and placing the removed last digits as "leaves" on the right side to show the distribution of values. It provides examples of creating stemplots and discusses techniques like rounding stems or using split stems when data is not well-distributed along a single stem.
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This document provides step-by-step instructions for dividing a 3-digit number by a 2-digit number using long division. It uses the example of 895 divided by 15. It shows how to place the numbers in the division bar, find the closest multiple of the divisor to divide each column, bring down remaining digits, and provide the quotient and remainder. The full division is shown with a quotient of 59 and remainder of 10, so 895 divided by 15 equals 59 remainder 10.
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The document defines factors, multiples, and perfect numbers. Factors are numbers that divide evenly into a given number. Multiples are numbers that the given number divides into evenly. A perfect number is one where the sum of its factors is equal to twice the number. Examples given are that 6 is a perfect number because the factors of 1, 2, 3, and 6 sum to 12, which is twice 6.
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1) Decimals are a numbering system based on tens where a number is written as a whole number with a decimal point separating the whole number from fractional parts.
2) Decimals can be added, subtracted, multiplied, and divided following specific rules such as aligning decimal points and counting decimal places.
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1. The document explains how to divide a 3-digit number by a 1-digit number using long division, using the example of 895 divided by 5.
2. It works through the long division step-by-step, placing digits above the line and subtracting until there is no remainder.
3. The answer is that 895 divided by 5 equals 179 with no remainder.
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This document provides an introduction to integers. It defines integers as the set of counting numbers, their opposites, and zero. It discusses the concepts of absolute value and how it relates to adding and subtracting integers. Rules for adding, multiplying and dividing integers are presented, focusing on keeping track of signs to determine the final sign of the operation. Practice exercises are provided to help reinforce these concepts.
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The document provides an introduction to decimals. Students will learn what decimals are, that they have place values like whole numbers, and how to convert fractions and word problems to decimals. The class will identify decimal place values, convert fractions to decimals, and solve word problems involving decimals. They will then play a decimal wars game to practice comparing decimals.
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This document provides instructions for performing basic operations with decimals such as addition, subtraction, multiplication, and division. It explains how to align the decimals and describes the steps for each operation. Examples are provided for adding, subtracting, multiplying, and dividing decimals. The document also covers comparing and converting fractions and decimals, with examples of how to convert a fraction to a decimal and vice versa. It concludes with contact information.
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The document describes using a number line method to estimate square roots. It reviews perfect squares from 1 to 144. To estimate the square root of 40, it identifies the nearest perfect squares of 36 and 49 and draws a number line between them. It determines that the square root of 40 is closer to 6 than 7. Similarly, to estimate the square root of 58, it identifies the nearest perfect squares of 49 and 64 and draws a number line between them, determining the square root is closer to 8 than 7. It concludes by having the reader practice estimating square roots using the number line method.
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This document introduces decimals by showing fractions written as decimals from tenths to hundredths. It provides examples of fractions written out as decimals and compares the relative size of different decimals. Key concepts covered include how to write tenths, hundredths, and mixed numbers as decimals and comparing the value of decimals.
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This document discusses techniques from Vedic mathematics for quickly multiplying numbers mentally. It describes methods for multiplying by 11, 15, and single-digit numbers without using long multiplication. For two-digit numbers between 89-100, it shows how to subtract each number from 100 before multiplying the results and adding diagonally to find the full product. With practice, these methods allow for multiplying two-digit and some three-digit numbers mentally. Examples are provided to illustrate the techniques.
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The document discusses whole numbers and natural numbers. It defines natural numbers as counting numbers and notes that natural numbers along with zero form the set of whole numbers. It provides examples of finding predecessors and successors of numbers and using the number line to demonstrate addition, subtraction and multiplication of whole numbers. It poses questions about properties of natural numbers and whole numbers.
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Whole numbers include the natural numbers (1, 2, 3, etc.) and zero. They can be represented on a number line and have important properties - zero is the smallest whole number, there are an infinite number of whole numbers, and each whole number has a unique successor and predecessor obtained by adding or subtracting 1.
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This document provides step-by-step instructions for dividing a 3-digit number by a 2-digit number using long division. It uses the example of 895 divided by 15. It shows how to place the numbers in the division bar, find the closest multiple of the divisor to divide each column, bring down remaining digits, and provide the quotient and remainder. The full division is shown with a quotient of 59 and remainder of 10, so 895 divided by 15 equals 59 remainder 10.
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The document defines factors, multiples, and perfect numbers. Factors are numbers that divide evenly into a given number. Multiples are numbers that the given number divides into evenly. A perfect number is one where the sum of its factors is equal to twice the number. Examples given are that 6 is a perfect number because the factors of 1, 2, 3, and 6 sum to 12, which is twice 6.
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The document provides information about decimals, including:
1) Decimals are a numbering system based on tens where a number is written as a whole number with a decimal point separating the whole number from fractional parts.
2) Decimals can be added, subtracted, multiplied, and divided following specific rules such as aligning decimal points and counting decimal places.
3) Fractions can be converted to decimals by dividing the numerator by the denominator.
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1. The document explains how to divide a 3-digit number by a 1-digit number using long division, using the example of 895 divided by 5.
2. It works through the long division step-by-step, placing digits above the line and subtracting until there is no remainder.
3. The answer is that 895 divided by 5 equals 179 with no remainder.
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This document provides an introduction to integers. It defines integers as the set of counting numbers, their opposites, and zero. It discusses the concepts of absolute value and how it relates to adding and subtracting integers. Rules for adding, multiplying and dividing integers are presented, focusing on keeping track of signs to determine the final sign of the operation. Practice exercises are provided to help reinforce these concepts.
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This document provides instructions for performing basic operations with decimals such as addition, subtraction, multiplication, and division. It explains how to align the decimals and describes the steps for each operation. Examples are provided for adding, subtracting, multiplying, and dividing decimals. The document also covers comparing and converting fractions and decimals, with examples of how to convert a fraction to a decimal and vice versa. It concludes with contact information.
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The document discusses place value with decimals. It explains that the name of a decimal is based on the number of places to the right of the decimal point, with tenths, hundredths and thousandths as examples. Mixed decimals contain both whole numbers and decimals. To read decimals correctly, say "and" at the decimal point and read whole numbers to the left and fractional decimals to the right. Extra zeros after the decimal do not change a number's value. The document provides practice problems for writing decimals, identifying place values, writing decimals as words, and adding and subtracting decimals by lining up the decimals.
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The document describes using a number line method to estimate square roots. It reviews perfect squares from 1 to 144. To estimate the square root of 40, it identifies the nearest perfect squares of 36 and 49 and draws a number line between them. It determines that the square root of 40 is closer to 6 than 7. Similarly, to estimate the square root of 58, it identifies the nearest perfect squares of 49 and 64 and draws a number line between them, determining the square root is closer to 8 than 7. It concludes by having the reader practice estimating square roots using the number line method.
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Addition involves adding two or more numbers together. The plus sign '+' is used to denote addition. Larger numbers can be added in columns. The addition table provides a way to look up sums by going to the row of the first number and column of the second number. There are several strategies provided for adding numbers, such as jumping, adding up to ten, and doing the tens last. The topic of addition is continued in the next video.
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This document introduces decimals by showing fractions written as decimals from tenths to hundredths. It provides examples of fractions written out as decimals and compares the relative size of different decimals. Key concepts covered include how to write tenths, hundredths, and mixed numbers as decimals and comparing the value of decimals.
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The document provides step-by-step instructions for dividing a 3-digit number by a 1-digit number without remainder. It uses the example of dividing 741 by 3. The instructions are to place the larger number inside the division bar and the smaller number outside. Then divide the hundreds, tens, and ones columns sequentially, placing the quotients above and remainders beside the next column. Following these steps, the document arrives at the solution of 741 divided by 3 equals 247.
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Integers are defined as whole numbers that can be positive, negative, or zero, and are used to represent real-world situations involving amounts above and below zero like elevation, temperature, financial gains and losses, and distances. Integers are located on a number line and adding integers involves moving right on the number line while subtracting involves moving left, with examples provided of calculating distances between elevations represented as integers.
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Students will use their understanding of square numbers to evaluate square roots. Remember, square roots, quite literally mean going from square numbers, back to the root - the number which you multiplied in the first place to get the square number. Example: The square root of 49 is 7.
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みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
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Math trivia
- 1. The Sieve of AtkinThe Sieve of Eratosthenesare methods to determine whether a given integer is a prime number or not. Both methods can be applied and used to create programming algorithms and the computer will do the rest of the job for you. The Sieve of Eratosthenes is a simple way. Let say you want to find out which numbers (from 1 to 100) are prime numbers. So, first of all you need to list all the 100 numbers down. Then, you start crossing out numbers that are not prime numbers. First and foremost, 1 is crossed out because it is not a prime number. Next, 2 is circled since it is the smallest and the only even prime number. Cancel out any other even numbers because they are all multiples of 2. This will leave you with less numbers. Next, circle 3 and cross out any other numbers that are multiples of 3. The same routine is used and continued for the rest of the numbers until 100 and you will all the prime numbers you need. Meanwhile, the Sieve of Atkin is a newer and faster way. It is revised from the Sieve of Eratosthenes. The Sieve of Atkin is used generally in an algoritm, because it is very tedious and troublesome to work out the list manually. Game: Encircle all the PRIME NUNMBERS in the table. 1 11 21 31 41 51 61 71 81 91 Answer: 2 12 22 32 42 52 62 72 82 92 3 13 23 33 43 53 63 73 83 93 4 14 24 34 44 54 64 74 84 94 5 15 25 35 45 55 65 75 85 95 6 16 26 36 46 56 66 76 86 96 7 17 27 37 47 57 67 77 87 97 8 18 28 38 48 58 68 78 88 98 9 19 29 39 49 59 69 79 89 99 10 20 30 40 50 60 70 80 90 100
- 2. Trivia The "Greatest Common Factor" is often abbreviated to "GCF", and is also known as: the "Greatest Common Divisor (GCD)", or the "Highest Common Factor (HCF)" Answer: 4 Math Trivia #2: Least Common Multiples The least common multiple is the smallest number that is a multiple of two numbers. "A group of Girl Scouts goes to every 6th house to sell cookies. Another group goes to every 8th house. At which house will they first meet?" Answer: the 24th house. It is the least common multiple of 6 and 8. (6 * 4 = 24 and 8 * 3 = 24).
- 3. Answer: 24