This is the marking copy and it carries every answer. Her sheet is the other file — same numbering, same margin codes, so you can mark straight down the page.
Round the sum of 18.208 and 1.42 to the nearest whole number.
answer 20
method Add first, lining up the decimal points: 18.208 + 1.420 = 19.628. Then round to the nearest whole number — the digit after the point is 6, which is 5 or more, so round up to 20.
watch Rounding each number first (18 + 1 = 19). The question says round the SUM, and rounding early loses the 0.628 that pushes it over.
I am a 3-digit odd number. All my three digits are different. All my three digits are multiples of 3. The digit in the ‘hundreds’ place is twice the digit in the ‘ones’ place. What number am I?
answer 693
method The digits that are multiples of 3 are 3, 6 and 9. The number is odd, so the ones digit is 3 or 9. If the ones digit were 9, the hundreds digit would be 18 — not a digit. So the ones digit is 3 and the hundreds digit is 2 × 3 = 6. The tens digit must be a different multiple of 3, which leaves 9. The number is 693.
watch Counting 0 as a multiple of 3 and offering 603 as well. In primary work the multiples of 3 are 3, 6, 9, … — they start at 3, not 0.
What is the value of the digit ‘6’ in the numeral 36 574?
answer 6000
method Read the places from the right: 4 ones, 7 tens, 5 hundreds, 6 thousands, 3 ten-thousands. The 6 sits in the thousands place, so its value is 6 × 1000 = 6000.
watch Answering 6, or naming the place ("thousands") instead of the VALUE. The question asks what the digit is worth.
A 4-digit number is made up of three different odd digits and a zero. What is the smallest possible value of the number?
answer 1035
method The odd digits are 1, 3, 5, 7, 9 and three of them must be different. To make the number small, put the smallest digit first — but not the 0, because a 4-digit number cannot start with 0. So the thousands digit is 1, the hundreds digit is the 0, and the last two places take the next smallest odd digits: 3 then 5. That gives 1035.
watch Starting with 0 (0135 is a 3-digit number), or forgetting the three odd digits must be DIFFERENT and writing 1011.
A number when rounded to the nearest 100 is 8000. What is the greatest possible number?
answer 8049
method Rounding to the nearest 100 gives 8000 for anything from 7950 up to 8049. Anything from 8050 upwards rounds to 8100 instead. So the greatest is 8049.
watch Answering 8050 — that is the first number that rounds UP to 8100, not the last that rounds to 8000. Test the boundary by rounding it back.
What is the value of 20 thousands and 9 tens?
(A) 209 (B) 2009 (C) 20 009 (D) 20 090
answer (D) — 20 090
method Build the number place by place: 20 thousands is 20 000, and 9 tens is 90. Add them: 20 000 + 90 = 20 090.
watch Writing the 9 in the ones place (20 009). "Tens" means the second column from the right, so the 9 needs a 0 after it.
The digit 6 in 63 470 has the same value as __________.
(1) 6 × 10 (2) 6 × 100 (3) 6 × 1000 (4) 6 × 10 000
answer (4) — 6 × 10 000
method Read the places from the RIGHT: 0 ones, 7 tens, 4 hundreds, 3 thousands, 6 ten-thousands. So the 6 is worth 6 × 10 000 = 60 000.
watch Counting places from the left, or counting the digit's position ("it is the 1st digit") instead of its place value.
Using all the digits 8, 0, 9, 2, form the smallest multiple of 5.
(1) 2890 (2) 2980 (3) 8920 (4) 9820
answer (1) — 2890
method A multiple of 5 ends in 0 or 5. There is no 5 among the digits, so the number must end in 0. That leaves 8, 9 and 2 for the first three places, and the smallest arrangement of those is 2, 8, 9. So the number is 2890.
watch Forgetting that ALL four digits must be used, or trying to put the 0 first to make the number small.
The following numbers are arranged in descending order: A, 17 898, 8929, 879. A is a 5-digit odd number. What is the value of A?
(1) 17 791 (2) 18 642 (3) 27 424 (4) 71 889
answer (4) — 71 889
method Descending means A is the largest, so A must be GREATER than 17 898 — that rules out 17 791. A must also be odd, so it ends in 1, 3, 5, 7 or 9 — that rules out 18 642 and 27 424. Only 71 889 passes both tests.
watch Checking only that the number is odd and picking 17 791, forgetting A also has to be bigger than 17 898.
The table shows the number of customers at a restaurant over 4 days; part of it was covered by a stain. The number of customers on Day 3 is equal to the total number of customers on Day 1 and Day 2. The total number of customers on all 4 days is 240 when rounded to the nearest ten. What is the greatest possible number of customers on Day 4?
Day | Number of customers ----+-------------------- 1 | 30 2 | 45 3 | ##### stain ##### 4 | ##### stain #####
answer 94
method Day 3 = Day 1 + Day 2 = 30 + 45 = 75. So Days 1, 2 and 3 come to 30 + 45 + 75 = 150. The 4-day total rounds to 240 to the nearest ten, so the real total is anywhere from 235 to 244. The question wants the GREATEST Day 4, so take the greatest total: 244 − 150 = 94 customers.
watch Taking the total as exactly 240 and answering 90. "Rounds to 240" means a range (235 to 244), and the largest number in that range is what makes Day 4 largest.
In the number 56 748, add the value of the digit 5 to the value of the digit 4. What do you get?
(A) 9 (B) 54 (C) 5040 (D) 50 040 (E) 50 400
answer (D) — 50 040
method The 5 is in the ten-thousands place, so it is worth 50 000. The 4 is in the tens place, so it is worth 40. 50 000 + 40 = 50 040.