17. [Exploring Numbers]

Transcription

1 . [Exploring Numbers] Skill. Comparing whole numbers. Compare the size of the digits in the same place, one at a time. Work from left to right across each number. Q. Which number is the A ) 06 B ) 60 C ) 60 A. C Tens of thousands and thousands: All numbers have the same digit in the tens of thousands place (), and the same digit in the thousands place (). Hundreds: In the hundreds place is greater than 6. So A and C are greater than B. Tens: In the tens place 6 is greater than 0. So 60 is greater than 06. a) 80 > 80 True or false? 8 >... > means is greater than < means is less than compare the hundreds place true b) 0 < 0 True or false?... c) > True or false?... d) 9 < 9 True or false?... e) 60 > 60 True or false?... f) 8 > 8 True or false?... g) Which number is the A ) 80 B ) 80 C ) 800 > 0... compare the digits in the tens place B h) Which number is the A ) 0 9 B ) 0 9 C ) i) Which number is the A ) 9 0 B ) 9 0 C ) j) Which number is the A ) 80 B ) 08 C ) k) Which number is the A ) 6 0 B ) 6 0 C ) l) Which number is the A ) 09 B ) 90 C ) page 9 Maths Mate./. Skill Builder

2 Skill. Understanding and finding the place value of a digit in a number (). Compare the position of the digit to the position of the decimal point. Hint: There is a decimal point which is not written, at the end of any whole number. Place value Value tens of thousands thousands 6000 hundreds tens units tenths 0 hundredths 00 thousandths Decimal point Q. What is the value of the underlined digit in the number 6 8.? A Consider the position of the digit to that of the decimal point. is five places to the left so it is in the tens of thousands place. The represents tens of thousands or a) In the number 08 which digit is in the tens place? b) In the number 90 which digit is in the units place? c) In the number 86 which digit is in the hundreds place? d) In the number 08 which digit is in the thousands place? e) In the number 6. which digit is in the units place? f) In the number 0.0 which digit is in the hundredths place? g) In the number.809 which digit is in the tenths place? h) In the number 0.08 which digit is in the thousandths place? i) What is the value of the underlined digit in the number 9? tens.. 0 j) What is the value of the underlined digit in the number 0?.. k) What is the value of the underlined digit in the number 6 09? l) What is the value of the underlined digit in the number 86 9?.. page 0 Maths Mate./. Skill Builder

3 Skill. Understanding and finding the place value of a digit in a number (). m) What is the value of the underlined digit in the number? n) What is the value of the underlined digit in the number 06?.. o) What is the value of the underlined digit in the number 9 60?... p) What is the value of the underlined digit in the number 8?.. q) What is the value of the underlined digit in the number.0? hundredths = = r) What is the value of the underlined digit in the number.08? thousandths = = s) What is the value of the underlined digit in the number 0.98?.. = t) What is the value of the underlined digit in the number.06?.. = u) In which number does the digit have greater value? A ).6 B ) 0. A) value... B) value 0. > A v) In which number does the digit 6 have greater value? A ) 0 06 B ) 06 A)... B)... w) In which number does the digit have greater value? A ). B ).98 A)... B)... x) In which number does the digit 9 have greater value? A ) 90 B ) 0 89 A)... B)... y) In which number does the digit have greater value? A ) 8.9 B ). A)... B)... z) In which number does the digit have greater value? A ) 0.6 B ) 0.6 A)... B)... page Maths Mate./. Skill Builder

4 Skill. Writing word numbers as numerals. Write the digits in order. Leave a space between the thousands and the hundreds, and between the millions and the hundreds of thousands. Write a zero in any place that is left empty between other digits. Q. Express in numerals: fifty thousand, six hundred and nine A Tens of Th. Th. 0 H T U First write 0 for the words fifty thousand, then write a comma. Write the digit 6 for the hundreds, then write the digit 0, because there are no tens. Finally write the digit 9 for the units. a) Express in numerals: two hundred and fifteen c) Express in numerals: six thousand and eighty-two e) Express in numerals: nine hundred and two g) Express in numerals: two hundred and ninety-eight i) Express in numerals: five hundred and thirty k) Express in numerals: seven hundred and fourteen m) Express in numerals: sixty thousand, five hundred and forty o) Express in numerals: four hundred and three thousand, two hundred q) Express in numerals: one million, nine hundred thousand and twenty-six b) Express in numerals: four thousand, one hundred and fifty d) Express in numerals: eight thousand, one hundred and seventeen f) Express in numerals: three thousand, four hundred h) Express in numerals: seven thousand, three hundred and nine j) Express in numerals: twelve thousand, six hundred l) Express in numerals: fourteen thousand and sixty-three n) Express in numerals: thirty-one thousand and seven p) Express in numerals: eight hundred thousand and fifty r) Express in numerals: seven million, six hundred thousand and forty page Maths Mate./. Skill Builder

5 Skill. Writing whole numbers in words (). Start from left and write the word for each digit (unless it is a 0), followed by its place value. Do not write anything for any 0 s. 00 = two hundred To write -digit numbers in words Use a hyphen (-) to separate the word for the tens from the word for the units, for all numbers from to 99; e.g. 6 is written as sixty-seven. Hint: Some -digit numbers have names that do not follow the usual rules. Use the following: 0 ten 0 fifty 90 ninety fourteen 8 eighteen 0 twenty 60 sixty eleven fifteen 9 nineteen 0 thirty 0 seventy twelve 6 sixteen 0 forty 80 eighty thirteen seventeen To write -digit numbers in words Describe the number of hundreds first. Always write hundred not hundreds. Write and after the word hundred, if other values follow. To write -digit numbers in words Describe the number of thousands first. Always write thousand not thousands. Write and between the word thousand and the following numerals when hundreds are missing. To write -digit numbers in words Describe the number of thousands by following the rules for -digit numbers. To write 6-digit numbers in words Describe the number of thousands by following the rules for -digit numbers. word first! place next Q. Write the number 069 in words. A. seven thousand and sixty-nine Th. H T U thousands, 0 hundreds, 6 tens and 9 units become in words: seven thousand and sixty-nine a) Write the number 8 in words. b) Write the number 6 in words. three hundred and eighteen c) Write the number 90 in words. d) Write the number in words. e) Write the number 06 in words. f) Write the number 0 in words. page Maths Mate./. Skill Builder

6 Skill. Writing whole numbers in words (). g) Write the number 800 in words. h) Write the number 609 in words. i) Write the number 0 in words. j) Write the number 600 in words. k) Write the number 00 in words. l) Write the number 00 in words. m) Write the number 00 in words. n) Write the number 0 in words. o) Write the number 800 in words. p) Write the number 000 in words. q) Write the number in words. r) Write the number in words. s) Write the number 0 00 in words. t) Write the number 00 in words. u) Write the number 090 in words. v) Write the number 008 in words. w) Write the number in words. x) Write the number in words. y) Write the number in words. z) Write the number in words. page Maths Mate./. Skill Builder

7 Skill. Rounding whole numbers to a given place. Circle the digit to the right of the requested place. If this digit is 0,,, or (< ) - round down - keep the digit in the requested place the same., 6,, 8 or 9 ( ) - round up - add to the digit in the requested place. Keep the number of digits in the answer the same as in the question by using zeros to fill the vacated spaces. Q. Round 06 to the nearest hundred. A. 00 Th. H T U 0 6 Th. H T U 0 0 The digit to the right of the hundreds place is 6. 6 so round up. Add to the 0 in the hundreds place to make. Put zeros in the tens and units places. a) Round 60 to the nearest thousand. < round down 60 by keeping... c) Round to the nearest hundred. 000 b) Round to the nearest ten... d) Round 806 to the nearest ten... e) Round to the nearest ten... f) Round 0 to the nearest thousand.... g) Round 6 to the nearest hundred. h) Round 6 to the nearest thousand.... i) Round 90 to the nearest ten. k) Round 0 06 to the nearest thousand.... j) Round 9 to the nearest hundred. l) Round 60 to the nearest hundred.... m) Round 68 to the nearest ten... n) Round 60 to the nearest hundred.... page Maths Mate./. Skill Builder

8 Skill.6 Ordering decimal numbers. Line up the decimal numbers at their decimal points. Compare digits in the same places, starting from the left, until you find the smallest digit. Hint: The number with the smallest digit will be the smallest number. Look for the second smallest number. Continue in this way until you find the largest number. Q. Place in ascending order: 0., 0.0, 0.0, 0.0 rd smallest st nd largest th units U. T HTh 0 0 tenths hundredths thousandths A. 0.0, 0.0, 0., 0.0 Find the smallest digits. Work from left to right. Units: all 0 Tenths: 0 < < so 0.0 is the smallest 0.0 is the largest either 0.0 or 0. is the nd smallest Hundredths: 0 < so 0.0 is the nd smallest 0. is the rd smallest a) Place in order from largest to smallest: 0.096, 0.69, 0.609, 0.09 U. T HTh the largest number the smallest number b) Place in ascending order: 0.0, 0., 0.0, 0.0 U. T HTh c) Place in ascending order: 0.08, 0.08, 0.08, 0.8 d) Place in descending order: 0., 0., 0.0, 0. e) Place in ascending order: 0.80, 0.0, 0.8, 0.08, 0.08 f) Place in order from smallest to largest: 0.6, 0.06, 0.6, 0., 0.0 g) Place in order from largest to smallest: 0.9, 0.09, 0.09, 0.0, 0. h) Place in ascending order: 0.6, 0.0, 0., 0.06, 0.06 page 6 Maths Mate./. Skill Builder

9 Skill. Comparing and ordering fractions. Find the least common denominator of the fractions, which is the Lowest Common Multiple (LCM) of the denominators. Change the fractions to equivalent fractions with the lowest common denominator. Arrange the fractions in order of the numerators (the smallest fraction has the smallest numerator and so on). smallest numerator = smallest fraction < 6 < 6 6 same denominator Hint: If unsure which is the LCM of the denominators, use their product as the common denominator. When the smaller denominators divide evenly into the biggest denominator, this biggest number becomes the common denominator. Q. Place in ascending order: A.,,,,,, 6 = = 0 0 = LCM of, and is = < 8 < 0, so < < or < < a) Which fraction has greater value? or LCM of 8 and is = = < b) Which fraction has greater value? or 8... c) Which fraction has greater value? d) Which fraction has greater value? or or e) Place in order from smallest to largest: LCM of, 8 and,, is 8 = = 0 = f) Place in order from largest to smallest: 9,, page Maths Mate./. Skill Builder

10 Skill.8 Rounding decimal numbers to a given place. To round a decimal number to the nearest whole number Circle the first digit after the decimal point. If this digit is: 0,,, or (< ) - round down - keep the unit digit unchanged and drop all the digits after the decimal point., 6,, 8 or 9 ( ) - round up - add to the unit digit and drop all the digits after the decimal point. To round a decimal number to a given place (One decimal place means tenths, two decimal places means hundredths and three decimal places means thousandths.) Circle the digit to the right of the requested place. If this digit is: 0,,, or (< ) - round down - keep the digit in the requested place unchanged and drop all following digits., 6,, 8 or 9 ( ) - round up - add to the digit in the requested place and drop all following digits. Q. Round. to the nearest whole number. A. Units Tenths Hundredths Units Tenths Hundredths 0 0 a) Round. to the nearest whole number. < round down. by keeping c) Round.8 to the nearest whole number. The first digit after the decimal point is. so round up. Add to the in the units place to make. Omit the digits after the decimal point. b) Round.9 to the nearest whole number. d) Round.68 to the nearest whole number. e) Round.86 to three decimal places. 6 round up by.86 adding to... g) Round 0.9 to one decimal place. f) Round 8.68 to two decimal places. h) Round 9.8 to one decimal place. i) Round.8 to two decimal places. j) Round to three decimal places. k) Round 0. to one decimal place. l) Round to three decimal places. page 8 Maths Mate./. Skill Builder

11 Skill.9 Recognising whole numbers and integers. INTEGERS Negative integers Zero Positive integers WHOLE NUMBERS Whole Numbers Negative integers, fractions and decimals are not whole numbers apart from these situations: ) Any positive fraction whose numerator is divisible by the denominator. = ) Any positive decimal with only zeros after the decimal point = 8 Q. Choose the whole numbers from this list: 6 9, 8.,,,, 0 a) Choose the whole numbers from this list: 9 68,,, 0., 68, c) Choose the whole numbers from this list:, 9, 9,.86, 0 e) Choose the integers from this list:,,., 8, 60 Integers Fractions and decimals are not integers, apart from these situations: ) Any fraction whose numerator is divisible by the denominator. ) Any decimal with only zeros after the decimal point. =.00 = A. 9 is negative, so not a whole number 8. is a decimal, so not a whole number 6 = 6 = is a whole number is a fraction, so not a whole number 6 So,, 0 are whole numbers. b) Choose the whole numbers from this list:,, 00,., 98 6 d) Choose the whole numbers from this list: ,, 0,, f) Choose the integers from this list:,,,., 00 9 g) Choose the integers from this list: 6,, 0., 0, 8 h) Choose the integers from this list:,.8,,, 0 i) Choose the integers from this list: 0.68,,,, 09 j) Choose the integers from this list: 0 0,,, 6., 000 page 9 Maths Mate./. Skill Builder

12 Skill.00 Recognising rational numbers. Rational Numbers Include all Integers, 0, 00,, all Fractions,, 8 00 all Terminating decimals.6,.69 all Square roots of perfect squares 9, 6 Q. Which numbers are rational? A. A) 0. is rational (terminating decimal) A ) 0. B ) π B) π is not rational (an infinite non-repeating decimal) C ) D ) 6 C) is not rational (square root of a prime number) D) 6 is rational (negative integer) So A and D are rational. a) Choose the rational numbers from the list: b) Choose the rational numbers from the list: π 8,,.9, π, 0,, 0.,, 0 6 c) Choose the rational numbers from the list: d) Choose the rational numbers from the list: 9,., 80,,, 98,.890, 69 0, 9 e) Which numbers are rational? A ) 0 B ) π C ). D ) 8 and f) Which numbers are rational? A ) π B ) C ) D ) 0 and g) Which numbers are rational? A ) 8. B ) C ) D ) π and h) Which numbers are rational? A ) B ) π C ) D ) 800 and i) Which is not a rational number? A ) B ) 60 C ).8 D ) 9 j) Which is not a rational number? A ) 0.08 B ) 996 π C ) D ) page 0 Maths Mate./. Skill Builder