Find the number halfway between 70 and 88
Worked Solution & Answer
(70 + 88) ÷ 2 = 79 B1
Answer: 79
Place Value — Notes & Worked Examples Show / Hide
Explanation:
The position of a digit in a number determines its place value: Thousands (1000), Hundreds (100), Tens (10), Units (1), Tenths (0.1 or 110), Hundredths (0.01 or 1100), and Thousandths (0.001).
When multiplying by 10, 100, or 1000, the digits move 1, 2, or 3 places to the left (making the number bigger). When dividing by 10, 100, or 1000, the digits move 1, 2, or 3 places to the right. Use this to adapt a given calculation.
Example 1: For the number 47 308.29, write down the value of: (a) the digit 7 (b) the digit 9
Solution:
(a) The digit 7 is in the thousands column:
• Value = 7000 (or seven thousand)
(b) The digit 9 is in the hundredths column:
• Value = 0.09 (or 9100, nine hundredths)
Answers: (a) 7000 (b) 0.09
Example 2: Given that 46 × 38 = 1748, write down the value of: (a) 4.6 × 3.8 (b) 174.8 ÷ 38
Solution:
(a) 46 is divided by 10 and 38 is divided by 10:
• Divide 1748 by 100 (10 × 10) → 17.48
(b) Since 1748 ÷ 38 = 46, and 174.8 is 10 times smaller:
• Divide 46 by 10 → 4.6
Answers: (a) 17.48 (b) 4.6
Fill in the missing number on the number line
25, 30, 35, \hspace{0.8cm}, 45
25, 30, 35, \hspace{0.8cm}, 45
Worked Solution & Answer
Step size is +5, so 35 + 5 = 40 B1
Answer: 40
Here are four digits.
7 3 4 9
7 3 4 9
(a) Use three of these digits to write down the largest possible 3-digit number. [1 mark]
(b) Here are four different digits. [1 mark]
8 2 1 6
Put one of these digits in each box to give the smallest possible answer to the sum.
You must use each digit only once.
Put one of these digits in each box to give the smallest possible answer to the sum.
You must use each digit only once.
Worked Solution & Answer
(a)
9, 7, 4 gives 974 B1
Answer (a): 974
(b)
Put 1 and 2 in the tens columns: 16 + 28 = 44 (or 18 + 26 = 44) B1
Answer (b): 16 + 28 (or 18 + 26)
Here are four cards.
Each card has a number written on it.
Each card has a number written on it.
(a) Arrange the four cards to make the largest possible even number. [1 mark]
(b) Find this difference. [2 marks]
Worked Solution & Answer
(a)
Even digit 4 at end, largest remaining in descending order: 7534 B1
Answer (a): 7534
(b)
Closest number is 3574 M1
3600 – 3574 = 26 A1
3600 – 3574 = 26 A1
Answer (b): 26
The table gives information about the weight of sugar produced by each of five countries in one year.
(a) Write the number 28 149 in words. [1 mark]
(b) Which of these five countries produced the greatest weight of sugar? [1 mark]
(c) Write down the value of the 8 in the number 23 787 [1 mark]
(d) Write the number 15 745 correct to the nearest thousand. [1 mark]
Worked Solution & Answer
(a)
28 149 in words C1
Answer (a): Twenty-eight thousand, one hundred and forty-nine
(b)
592 668 (Kenya) is largest B1
Answer (b): Kenya
(c)
8 is in tens column = 80 B1
Answer (c): 80
(d)
15 745 → 16 000 B1
Answer (d): 16 000
(a)(i) [ ] + 357 = 486 (1) (ii) [ ] × 23 = 1840 (1) (b) Cards 2, 7, 4, 5: (i) Smallest 4-digit number (1) (ii) Even 4-digit number (1)
(a) [1 mark]
(b) [1 mark]
(b) Show how the cards can be arranged to make the smallest number using all four cards. [1 mark]
(d) Show how the cards can be arranged to make an even number using all four cards. [1 mark]
Worked Solution & Answer
(a)
486 – 357 = 129 B1
Answer (a): 129
(b)
1840 ÷ 23 = 80 B1
Answer (b): 80
(b)
Ascending digits: 2, 4, 5, 7 → 2457 B1
Answer (b): 2457
(d)
Ends in 2 or 4, e.g. 2754 B1
Answer (d): 2754 (any 4-digit arrangement ending in 2 or 4)
The table shows the length, in kilometres, of the coastline of each of five oceans.
(a) Which of these oceans has the greatest length of coastline? [1 mark]
(b) Write the number 17 968 in words. [1 mark]
(c) Write the number 66 526 correct to the nearest thousand. [1 mark]
(d) Work out the total length of the coastlines of the Arctic Ocean and the Pacific Ocean. [1 mark]
kilometres
Worked Solution & Answer
(a)
135 663 is largest B1
Answer (a): Pacific
(b)
Seventeen thousand nine hundred and sixty eight
Answer (b): Seventeen thousand nine hundred and sixty eight
(c)
66 526 → 67 000 B1
Answer (c): 67 000
(d)
45 389 + 135 663 = 181 052 B1
Answer (d): 181 052 kilometres
Nav found the following table that shows the age, in years, of each of seven cities.
(a) Write down the name of the city with the greatest age. [1 mark]
(b) Write the number 2534 in words. [1 mark]
(c) Write the number 2351 correct to the nearest ten. [1 mark]
(d) Work out the difference between the age of Cadiz and the age of Nanjing. [1 mark]
years
(e) What is the age of Jenin in whole millenniums? [1 mark]
millenniums
Worked Solution & Answer
(a)
5669 is largest B1
Answer (a): Gaziantep
(b)
Two thousand, five hundred and thirty-four
Answer (b): Two thousand, five hundred and thirty-four
(c)
2350
Answer (c): 2350
(d)
3124 – 2516 = 608 B1
Answer (d): 608 years
(e)
4469 ÷ 1000 = 4 whole millenniums B1
Answer (e): 4 millenniums
The table shows the distance, in kilometres, from London to each of five cities.
(a) Write the number 9280 in words. [1 mark]
(b) Which of the five cities is nearest to London? [1 mark]
(c) Write down the value of the 7 in 10 734 [1 mark]
(d) Which of the five cities is **seven thousand nine hundred and sixty two** kilometres from London? [1 mark]
(e) Write the number 16 983 correct to the nearest thousand. [1 mark]
Worked Solution & Answer
(a)
Nine thousand two hundred and eighty
Answer (a): Nine thousand two hundred and eighty
(b)
Smallest distance is 5567 (New York) B1
Answer (b): New York
(c)
7 hundreds = 700 B1
Answer (c): 700
(d)
7962 = Kolkata B1
Answer (d): Kolkata
(e)
16 983 → 17 000 B1
Answer (e): 17 000
Cho finds this information about the areas, in square kilometres, of some South American countries.
(a) Which of these countries has the largest area? [1 mark]
(b) Write the number 163 800 in words. [1 mark]
(c) Write down the value of the 7 in the number 406 752 [1 mark]
(d) Write the number 173 626 correct to the nearest thousand. [1 mark]
(e) Work out the difference between the area of Chile and the area of Uruguay. [1 mark]
square kilometres
Worked Solution & Answer
(a)
926 690 = Venezuela B1
Answer (a): Venezuela
(b)
One hundred and sixty-three thousand, eight hundred
Answer (b): One hundred and sixty-three thousand, eight hundred
(c)
700 (or 7 hundreds)
Answer (c): 700 (or 7 hundreds)
(d)
174 000
Answer (d): 174 000
(e)
756 100 – 173 626 = 582 474 B1
Answer (e): 582 474 square kilometres