1 In the table, look at the given starting number and whether to count forwards or backwards. In the specified multiples, what are the first five numbers you reach? The first one has been done for you.
Negative numbers
Sometimes numbers can be negative. These are numbers that are less than zero. e.g. In winter, an outside temperature may drop below zero, to −5°C. On a number line, negative numbers are to the left of zero.
2
Fill in the missing numbers on the number line.
3 Place the following numbers on the number line: 30, 60, –40, –80, 90, –10
Count forwards or backwards using the information given. The first one has been done for you.
Number | Number structures
Topic 1.2 Rounding
Rounding numbers
Before a number is rounded, you need to know which place value column you are rounding to. For example, if you wanted to round 32,828 to the nearest thousand, you focus on the digit to the right of it. Here’s how:
We can see that the circled digit is more than 5. So, we round up to the nearest thousand. 32,828 rounded to the nearest thousand is 33,000. (All the columns to the right are now empty. So, a zero goes in each empty space.)
Learn
The ABC of rounding Decideon thecolumn youare roundingto.
Circlethe digittothe right.
Tththhto 32828
Ifthedigit is5or more, roundUP
1 Round the numbers below to the nearest 100.
2 Round these numbers to the nearest 1,000. a 5,793
3 Round these numbers to the nearest 10,000.
Ifthedigit is4orless, round DOWN
4 A factory makes roughly 5,000 cars in one day (rounded to the closest thousand).
Using the numbers, list three possible numbers that could be the actual number of toy cars produced at this factory.
1, 5, 6, 4, 7, 2
5 Round these numbers to the nearest thousand.
a 1,875 b 4,125
c 19,235 d 56,852
e 996 f 3,599
g 32,828 h 824,721
6 Round 32,828 to the nearest:
a hundred b thousand
c ten d ten thousand.
7 If a prize of $22,935 had to be rounded, would you prefer it to be rounded to the nearest ten thousand, thousand, hundred or ten? Give a reason for your answer.
8 Round to the nearest ten thousand.
a 38,759 b 52,811
c 41,445 d 97,624
e 25,555 f 872,923
g 451,445 h 375,172
9 Round to the nearest hundred thousand.
a 178,280 b 292,321
c 413,633 d 928,872
e 298,729 f 562,837
g 1,132,405 h 7,234,116
1 Round to the nearest tenth.
a 1.82
c 0.48
2.87 e 37.09
3.55 g 7.99
0.82
i 4.47 j 34.21 k 21.18 l 98.78
2 In New Zealand, our smallest coin is 10 cents. Round these money amounts to the nearest 10 cents (tenth). a $7.82
3 Scientists say that the Moon is an average of 384,399 kilometres away from Earth.
a What would be your rounded distance to the Moon? Give a reason for the way you have rounded the distance.
b Why do you think the average distance is given and not the exact distance?
Rounding to the nearest million!
4 Circle the correct rounding, from either the left or the right column. 2,000,000
Deepen
1 This table shows unusual record-breaking activities.
USA Number of dogs on a walk together
New ZealandPeople performing the Haka
Poland People ringing bells together
Hong KongPeople playing percussion instruments together
Singapore People line dancing together
Portugal People making a human advertising sign
Mexico People doing aerobics at the same time
India Trees planted by a group in one day
USA People in a conga line
England The longest scarf ever knitted (in centimetres)
Complete the number column in the table by rewriting the numbers in order, from the lowest to the highest number. The events are in order from low to high.
2 The following numbers are from the list in question 1. They have been rounded in various ways. Write the actual number for each.
a 80,000
c 3,000
b 40,000
d 300,000
e 10,100 f 10,000
g 100,000
i 7,000
DRAFT
h 12,000
j 35,000
3 Rounded to the nearest ten thousand, the 2024 population of New Plymouth in the North Island was 50,000 people. The actual number can be made by using each of these digits once: 1 4 6 8 9
List as many of the 18 numbers that could be the actual population as you can.
Improving your estimating and rounding skills can help you save time with mental calculations.
4
Look at these facts and figures. Show how you would round the numbers by underlining or highlighting one of the numbers.
a Krubera: the deepest cave in the world 2,191 m 2,100 or 2,200?
b Cehi: the tenth-deepest cave in the world 1,502 m 1,500 or 1,600?
c Mont Blanc: the highest mountain in Europe 4,807 m 4,800 or 4,900?
d Mont Maudit: the tenth-highest mountain in Europe 4,466 m 4,400 or 4,500?
e Mt Everest: the highest mountain in the world 8,850 m 8,800 or 8,900?
f Aoraki/Mount Cook, the highest mountain in NZ 3,754 m 3,700 or 3,800?
g Mammoth Cave: the longest cave in the world 590,600 m 500,000 or 600,000?
h Wind Cave: the fourth-longest cave in the world 212,500 m 200,000 or 300,000?
5 Circle the number that will make the information correct.
a The total of the depths of Krubera and Cehi caves is about 3,500 m, 3,700 m, 3,600 m, 3,400 m.
b Mont Blanc is about 20 m, 200 m, 30 m, 300 m taller than Mont Maudit.
c If you walked the lengths of the Mammoth Cave and the Wind Cave, you would have travelled about 700 km, 70 km, 80 km, 800 km.
6 Sarah goes shopping in a bargain shop. She has $11 to spend. She goes to the checkout with the following items.
