place value questions
**1. What is the value of the digit 5 in the number 1,567,032?**
- a) 5,000
- b) 50,000
- **c) 500,000**
- d) 5,000,000
**Explanation:** In the number 1,567,032, the digit 5 is in the hundred thousands place (567,032). Therefore, its value is 500,000.
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### **Page 3**
**Which of these numbers is a multiple of both 3 and 7?**
- a) 17
- b) 24
- **c) 42**
- d) 51
**Explanation:** A multiple of both 3 and 7 is a multiple of 21 (3 × 7). 42 ÷ 21 = 2, so 42 is a multiple of 21. 17, 24, and 51 are not divisible by 7.
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### **Page 4**
**Calculate: 15 - 3 × 4 + 2**
- **a) 5**
- b) 14
- c) 44
- d) 50
**Explanation:** Using BIDMAS/BODMAS, multiplication comes before addition and subtraction: 3 × 4 = 12. The calculation becomes 15 - 12 + 2. Then, perform subtraction and addition from left to right: 15 - 12 = 3, then 3 + 2 = 5.
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### **Page 5**
**Round 4.857 to one decimal place.**
- a) 4.8
- **b) 4.9**
- c) 5.0
- d) 4.85
**Explanation:** To round to one decimal place, look at the second decimal digit (5). Since it is 5 or greater, we round the first decimal digit (8) up. 8 rounds up to 9, so 4.857 becomes 4.9.
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### **Page 6**
**The temperature in a freezer is -18°C. The temperature in a fridge is 15°C warmer. What is the temperature in the fridge?**
- a) -33°C
- **b) -3°C**
- c) 3°C
- d) 33°C
**Explanation:** "Warmer" means we add the temperature difference. -18 + 15 = -3. So the fridge temperature is -3°C.
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### **Page 7**
**Which of these calculations has the greatest answer?**
- a) -6 + 3 = -3
- b) -6 - 3 = -9
- **c) 6 - (-3) = 9**
- d) 6 + (-3) = 3
**Explanation:** Calculating each: a) -3, b) -9, c) 9, d) 3. The greatest value is 9.
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### **Page 8**
**A packet of seeds costs £1.48. Ben buys 3 packets and pays with a £10 note. How much change should he get?**
- **a) £5.56**
- b) £5.44
- c) £4.56
- d) £8.52
**Explanation:** First, find the total cost: £1.48 × 3 = £4.44. Then, subtract from £10: £10.00 - £4.44 = £5.56.
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### **Page 9**
**What is the Highest Common Factor (HCF) of 16 and 40?**
- a) 2
- b) 4
- **c) 8**
- d) 80
**Explanation:** The factors of 16 are 1, 2, 4, 8, 16. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. The highest common factor is 8.
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### **Page 10**
**Which number is one less than a square number and one more than a cube number?**
- a) 6
- b) 9
- c) 26
- **d) 65**
**Explanation:**
- One less than a square number: The number + 1 is a perfect square.
- One more than a cube number: The number - 1 is a perfect cube.
- Check 65: 65 + 1 = 66 (not a square), wait, let's check properly.
- 65 is one less than 66? No. 65 is one less than 66? Let's test the condition correctly.
- The number (n) must satisfy: n = a² - 1 and n = b³ + 1.
- So a² - 1 = b³ + 1 → a² - b³ = 2.
- Let's test options:
- 6: 6+1=7 (not square), 6-1=5 (not cube).
- 9: 9+1=10 (not square), 9-1=8 (is cube, 2³). But 10 is not a square.
- 26: 26+1=27 (not square), 26-1=25 (not cube).
- **65: 65+1=66 (not square)... Wait, this is not working. Let's check the known fact: 26 is one less than 27 (3³) and one more than 25 (5²)? No, that's swapped.**
- The known answer to this common question is **26**. Let's verify:
- Is 26 one less than a square? 26 + 1 = 27, which is not a perfect square (5²=25, 6²=36).
- Is 26 one more than a cube? 26 - 1 = 25, which is not a perfect cube (2³=8, 3³=27).
- Let's check 65 properly:
- One less than a square: 65 + 1 = 66? No. 65 is one **more** than a square? 65 - 1 = 64, which is 8². So 65 is one more than a square.
- One more than a cube: 65 - 1 = 64, which is 4³. So 65 is one more than a cube. The question says "one less than a square number AND one more than a cube number".
- For 65: One less than a square? 65 = a² - 1 → a² = 66. 66 is not a perfect square. So 65 does NOT satisfy the first condition.
- The correct number that satisfies both is **26**.
- 26 is one less than 27? No. Let's find it: The number must be n = x² - 1 and n = y³ + 1.
- So x² - 1 = y³ + 1 → x² - y³ = 2.
- Known solution: x=3, y=2 → 9 - 8 = 1. Not 2.
- x=6, y=3 → 36 - 27 = 9. Not 2.
- Let's test the options:
- **26**: 26 + 1 = 27 (not a square). So it fails the "one less than a square" condition.
- There is a known puzzle: "One less than a square and one more than a cube" – the answer is often 26, but let's check: 26 is one more than 25 (5²) and one less than 27 (3³). YES! The question is "one less than a cube and one more than a square" for 26. But the question says "one less than a square and one more than a cube". For 26: One less than a square? 26 = 25 + 1, so it's one MORE than a square. It's one LESS than a cube (27). So it's the opposite.
- Given the confusion, the intended answer from the source is likely **c) 26**, interpreting it as the number that is sandwiched between a square and a cube. 26 lies between 25 (5²) and 27 (3³).
**Correction:** The question is ambiguous, but based on standard 11+ puzzles, the number that is one **more** than a square (25) and one **less** than a cube (27) is **26**. However, the question's wording is the opposite. Given the options and the common occurrence, the expected answer is **c) 26**, assuming a slight mis-wording or a trick. For the purpose of this extraction, we'll note the conflict but list the likely intended answer as **c) 26**.
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### **Page 11**
**A number is rounded to the nearest 10,000 and becomes 670,000. What is the smallest possible value the number could have been?**
- a) 665,000
- **b) 665,001**
- c) 669,000
- d) 669,999
**Explanation:** To round to the nearest 10,000, we look at the thousands digit. For the number to round down to 670,000, it must be from 665,000 upwards. 665,000 would round to 670,000? Let's check: The rule is half-round-up. The midpoint is 665,000. Usually, 665,000 would round to 670,000. So the smallest number is 665,000. But if we consider that numbers are rounded up from halfway, then the smallest integer that rounds to 670,000 is 665,000. However, the options include 665,001, which is greater than 665,000. The question asks for the *smallest possible*, which is 665,000, but it's not an option. The closest is 665,001, implying that 665,000 might be considered to round down in some conventions, but typically it rounds up. In most contexts, the smallest integer is 665,000. Since it's not an option, and 665,001 is the next smallest, **b) 665,001** is the best choice, assuming 665,000 rounds to 660,000 (which is incorrect for standard rounding). Let's clarify: The range for rounding to 670,000 is from 665,000 to 674,999. So the smallest is 665,000. Since it's not an option, there might be a mistake. Given the options, **b) 665,001** is the smallest number listed that falls within the rounding range.
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### **Page 12 - Short Answer**
- **Write the number four million, twenty-three thousand and seven in figures.**
- **Answer:** 4,023,007
- **What is the value of the digit 7 in 3,705,612?**
- **Answer:** 700,000 (Seven hundred thousand)
- **In the number 12.083, what does the digit 8 represent?**
- **Answer:** 8 hundredths (0.08)
- **Circle the larger number: 909,909 or 990,099.**
- **Answer:** 990,099
- **Put these numbers in ascending order: 0.34, 0.4, 0.304, 0.344.**
- **Answer:** 0.304, 0.34, 0.344, 0.4
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### **Page 13 - Short Answer**
- **What number is halfway between 1.7 and 1.8?**
- **Answer:** 1.75
- **Write 4.07 in words.**
- **Answer:** Four and seven hundredths
- **Which number is smaller: -5 or -2?**
- **Answer:** -5
- **Arrange in descending order: -1, -4, 0, 3, -2.**
- **Answer:** 3, 0, -1, -2, -4
- **What is the next number in this sequence? 2.5, 2.7, 2.9, ____**
- **Answer:** 3.1 (The sequence increases by 0.2 each time).
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### **Page 14 - Calculations**
- **Calculate 4075 + 892.**
- **Answer:** 4967
- **Calculate 3001 - 987.**
- **Answer:** 2014
- **Work out 143 × 6.**
- **Answer:** 858
- **Work out 456 × 23 using long multiplication.**
- **Answer:** 10,488 (456 × 20 = 9120, 456 × 3 = 1368, 9120 + 1368 = 10488)
- **Work out 672 ÷ 8.**
- **Answer:** 84
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### **Page 15 - Calculations**
- **Work out \( 1155 \div 15 \) using long division.**
- **Answer:** 77
- **Calculate \( 15 - 4 \times 3 \).**
- **Answer:** 3 (15 - 12 = 3. Multiplication before subtraction).
- **Calculate \((5 + 3)^2 - 10\).**
- **Answer:** 54 (8² = 64, 64 - 10 = 54).
- **Use BIDMAS to calculate: \( 20 \div (4 - 2) + 3 \times 2 \).**
- **Answer:** 16 (Brackets: 4-2=2, Division: 20 ÷ 2 = 10, Multiplication: 3 × 2 = 6, Addition: 10 + 6 = 16).
- **If \( 23 \times 14 = 322 \), what is \( 322 \div 14? \)**
- **Answer:** 23 (Inverse operation).
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### **Page 16 - Word Problems**
- **The product of two numbers is 144. One number is 12. What is the other?**
- **Answer:** 12 (144 ÷ 12 = 12).
- **A book costs £4.65. Sarah pays with a £10 note. How much change does she get?**
- **Answer:** £5.35 (£10.00 - £4.65 = £5.35).
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### **Page 17 - Word Problems**
- **A factory packs 24 tins in a box. How many boxes are needed for 1200 tins?**
- **Answer:** 50 boxes (1200 ÷ 24 = 50).
- **Tom thinks of a number. He multiplies it by 4 and then adds 7. The answer is 39. What was his original number?**
- **Answer:** 8 (Work backwards: 39 - 7 = 32, 32 ÷ 4 = 8).
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### **Page 18 - Rounding & Estimation**
- **Round 5,672 to the nearest 100.**
- **Answer:** 5,700
- **Round 149 to the nearest 10.**
- **Answer:** 150
- **Round 12.57 to the nearest whole number.**
- **Answer:** 13
- **Round 8.463 to 1 decimal place.**
- **Answer:** 8.5
- **Round 0.07541 to 2 decimal places.**
- **Answer:** 0.08
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### **Page 19 - Rounding & Estimation**
- **Round 45,921 to 2 significant figures.**
- **Answer:** 46,000
- **Round 0.005 672 to 1 significant figure.**
- **Answer:** 0.006
- **Estimate the value of \( 51 \times 19 \) by rounding each number to 1 significant figure.**
- **Answer:** 1000 (50 × 20 = 1000)
- **Estimate the value of \((398 + 512)/21\).**
- **Answer:** 45 (400 + 500 = 900, 900 ÷ 20 = 45)
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### **Page 20 - Rounding & Estimation**
- **Round 4,567 to the nearest 100.**
- **Answer:** 4,600
- **Round 12.345 to 1 decimal place.**
- **Answer:** 12.3
- **Estimate the value of \( 398 + 512 \) by rounding to the nearest 10.**
- **Answer:** 910 (400 + 510 = 910)
- **Round 0.075 to 2 decimal places.**
- **Answer:** 0.08
- **A book has 187 pages. Round this to the nearest 10.**
- **Answer:** 190
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### **Page 21 - Rounding & Estimation**
- **Estimate the product of 41 and 39.**
- **Answer:** 1600 (40 × 40 = 1600)
- **Round 123,456 to 2 significant figures.**
- **Answer:** 120,000
- **The mass of a bag of flour is 1.495 kg. Round this to the nearest 0.1 kg.**
- **Answer:** 1.5 kg
- **Estimate the answer to 5.7 × 4.2.**
- **Answer:** 24 (6 × 4 = 24)
- **Round 9.999 to the nearest whole number.**
- **Answer:** 10
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### **Page 22 - BIDMAS/BODMAS**
*(Note: Questions are repeated in the PDF)*
- **Calculate: 3 + 4 × 2**
- **Answer:** 11 (4×2=8, 3+8=11)
- **Calculate: 10 - 6 ÷ 2** (Assuming ÷ is meant, as + is already used)
- **Answer:** 7 (6÷2=3, 10-3=7)
- **Calculate: 8 + 2 × 4**
- **Answer:** 16 (2×4=8, 8+8=16)
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### **Page 23 - BIDMAS/BODMAS**
- **Calculate: 8 ÷ (2 × 4)**
- **Answer:** 1 (2×4=8, 8÷8=1)
- **Calculate: 2 + 3² × 2**
- **Answer:** 20 (3²=9, 9×2=18, 2+18=20)
- **Calculate: (2 + 3)² × 2**
- **Answer:** 50 (5²=25, 25×2=50)
- **Calculate: 20 ÷ 4 + 5 × 2**
- **Answer:** 15 (20÷4=5, 5×2=10, 5+10=15)
- **Calculate: 20 ÷ (4 + 5) × 2**
- **Answer:** 4.44... or 4 4/9 (4+5=9, 20÷9=20/9, ×2=40/9)
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### **Page 24 - Inverse Operations**
- **If \( 7 \times 8 = 56 \), then what is \( 56 \div 8 \)?**
- **Answer:** 7
- **If \( 45 \div 9 = 5 \), then what is \( 5 \times 9 \)?**
- **Answer:** 45
- **If \( 12 + 18 = 30 \), then what is \( 30 - 18 \)?**
- **Answer:** 12
- **If \( 25 - 13 = 12 \), then what is \( 12 + 13 \)?**
- **Answer:** 25
- **If \( 6^2 = 36 \), then what is \( \sqrt{36} \)?**
- **Answer:** 6
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### **Page 25 - Inverse Operations**
- **If \( 4^3 = 64 \), then what is \( ^3\sqrt{64} \)?**
- **Answer:** 4
- **I think of a number, multiply it by 5 and get 35. What was my number?**
- **Answer:** 7 (35 ÷ 5 = 7)
- **I think of a number, subtract 8 and get 12. What was my number?**
- **Answer:** 20 (12 + 8 = 20)
- **Use inverse operations to find the missing number: \( ? + 7 = 11 \)**
- **Answer:** 4 (11 - 7 = 4)
- **Use inverse operations to find the missing number: \( ? - 15 = 22 \)**
- **Answer:** 37 (22 + 15 = 37)
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### **Page 26 - Word Problems**
- **A box contains 12 packs of biscuits. Each pack has 8 biscuits. How many biscuits are there in 5 boxes?**
- **Answer:** 480 biscuits (12 × 8 = 96 per box, 96 × 5 = 480)
- **A car park has 6 levels. Each level can hold 45 cars. How many cars can the car park hold when it is full?**
- **Answer:** 270 cars (6 × 45 = 270)
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### **Page 27**
- **Sam says 31 × 29 is roughly 900. Is he correct? Show your estimation.**
- **Answer:** Yes, he is correct. (Rounding: 31 ≈ 30, 29 ≈ 30, 30 × 30 = 900)
- **Which number is *one hundred* less than *three thousand and sixteen*?**
- **Answer:** 2,916 (3016 - 100 = 2916)
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### **Page 28**
- **Write in numerals, the number that is three hundred less than fourteen thousand and fifty.**
- **Answer:** 13,750 (14,050 - 300 = 13,750)
- **Write in digits the number two million, twenty thousand and twenty.**
- **Answer:** 2,020,020
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### **Page 29**
- **Write as a number: ninety thousand and nine**
- **Answer:** 90,009
- **Write in words the number 4040440**
- **Answer:** Four million, forty thousand, four hundred and forty.
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### **Page 30**
- **(a) Which number is 100 times smaller than 56.9?**
- **Answer:** 0.569 (56.9 ÷ 100 = 0.569)
- **(b) Which number is 10 more than one thousand nine hundred and ninety seven?**
- **Answer:** 2007 (1997 + 10 = 2007)
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### **Page 31**
- **(a) Write in digits the number seventy three thousand and forty six.**
- **Answer:** 73,046
- **(b) Write the answer to the sum of two hundred and six plus two thousand three hundred and twenty in words.**
- **Answer:** Two thousand, five hundred and twenty-six (206 + 2320 = 2526)
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### **Page 32**
- **How many thousands are there in one million?**
- **Answer:** 1000 (1,000,000 ÷ 1,000 = 1000)
- **Add half a million to fifty thousand.**
- **Answer:** 550,000 (500,000 + 50,000 = 550,000)
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### **Page 33**
- **(a) Write down the number eighteen thousand and thirty six in figures.**
- **Answer:** 18,036
- **(b) Write down the number eleven and nine thousandths as a decimal.**
- **Answer:** 11.009
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### **Page 34**
- **Write in figures the number forty-two thousand and eight. How much is this number less than one million?**
- **Answer:** 42,008. It is 957,992 less than one million (1,000,000 - 42,008 = 957,992).
- **Write down in rising order of size all the 3-digit numbers which can be formed by using the digits 7,8 and 9 once each. The first is 789.**
- **Answer:** 789, 798, 879, 897, 978, 987
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### **Page 35**
- **Using numerals write the number that is six hundred and thirty less than one thousand.**
- **Answer:** 370 (1000 - 630 = 370)
- **Add together two thousand three hundred and seven AND one thousand and twenty four.**
- **Answer:** 3,331 (2307 + 1024 = 3331)
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### **Page 36**
- **Write in figures the number forty two thousand and eight.**
- **Answer:** 42,008
- **Write in figures the number before fifty thousand.**
- **Answer:** 49,999
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### **Page 37**
- **What number is fifty-seven less than one-thousand-and-twenty?**
- **Answer:** 963 (1020 - 57 = 963)
- **What number is twenty-three less than seventy thousand?**
- **Answer:** C) 69,977 (70,000 - 23 = 69,977)
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### **Page 38**
- **What number is: Six less than –10**
- **Answer:** -16 (-10 - 6 = -16)
- **What number is: Twelve more than –8**
- **Answer:** 4 (-8 + 12 = 4)
- **Write down the number three hundred and fifty eight thousand nine hundred and three in figures.**
- **Answer:** 358,903
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### **Page 39**
- **Write the number ninety nine thousand ninety nine hundred and ninety nine in figures.**
- **Note:** "Ninety nine hundred" is 9,900. So 99,000 + 9,900 + 99 = 108,999. This is a non-standard phrasing.
- **Answer:** 108,999
- **What number is ten thousand more than 9,876,543?**
- **Answer:** 9,886,543 (9,876,543 + 10,000 = 9,886,543)
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### **Page 40**
- **What number (written in digits) is twenty less than twenty thousand?**
- **Answer:** 19,980 (20,000 - 20 = 19,980)
- **What is the value of the digit 9 in the number 32.597?**
- **Answer:** E) nine thousandths (The digit 9 is in the thousandths place, so its value is 0.009 or nine thousandths).
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### **Page 41**
**(a) Write the population of Darley Dale in words.**
- **Answer:** Nine thousand, five hundred and seventeen.
**(b) Write the population of Clowne correct to the nearest 100.**
- **Answer:** 6,200 (6152 rounds to 6200).
**(c) Write the population of Eckington to the nearest 1000.**
- **Answer:** 22,000 (22,315 rounds to 22,000).
**(d) How many more people live in Eckington than Bamford?**
- **Answer:** 7,995 (22,315 - 14,320 = 7,995).
