Unit 5
Banding dan Susun Nombor
Bilangan buku di empat perpustakaan desa:
| Perpustakaan | Bilangan buku |
|---|---|
| Cempaka | 23 817 |
| Kenanga | 31 540 |
| Melur | 9 862 |
| Teratai | 31 405 |
比较和排列 = banding dan susun
要知道哪个数比较大，不能只看数字的样子，要按数位一位一位比较。学会比较以后，就可以把几个数从小到大（升序）或从大到小（降序）排好。
例子：比较 12 000 和 21 000，万位 1 比 2 小，所以 12 000 较小。
注意：比较以前先数一数每个数有几位。
compare and arrange = banding dan susun
To know which number is bigger, we compare digit by digit, place by place, instead of just looking at how the number looks. Once we can compare, we can arrange several numbers from smallest to largest (ascending) or from largest to smallest (descending).
Example: comparing 12 000 and 21 000, the ten thousands digits are 1 and 2, so 12 000 is smaller.
Watch out: before comparing, count how many digits each number has.
Langkah 1
Banding digit di tempat paling tinggi
Kenanga 31 540 dan Cempaka 23 817
从最高位比起 = banding dari tempat paling tinggi
两个数位数相同时，先比最左边的最高位（万位）。哪个数的万位数字大，这个数就大，后面的数位不用再看了。
例子：40 128 和 39 990 → 万位 4 比 3 大，所以 40 128 较大，即使后面的 9 很大也没关系。
注意：马来文说“较大”用 lebih besar daripada，“较小”用 lebih kecil daripada。
start from the highest place = banding dari tempat paling tinggi
When two numbers have the same number of digits, compare the leftmost digits first, in the ten thousands place. The number with the bigger digit there is the bigger number, and the other places do not matter.
Example: 40 128 and 39 990: 4 is bigger than 3, so 40 128 is bigger even though 39 990 has many 9s.
Watch out: in Malay, bigger than is lebih besar daripada and smaller than is lebih kecil daripada.
Langkah 2
Jika sama, banding tempat seterusnya
Kenanga 31 540 dan Teratai 31 405
| puluh ribu | ribu | ratus | puluh | sa |
|---|---|---|---|---|
| 3 | 1 | 5 | 4 | 0 |
| 3 | 1 | 4 | 0 | 5 |
3 = 3 → 1 = 1 → 5 > 4
相同就比下一位 = jika sama, banding tempat seterusnya
最高位相同的时候，比不出大小，就往右移一位再比；还是相同，就再往右。第一个出现不同数字的数位，决定了哪个数大。
例子：56 219 和 56 291 → 万位、千位、百位都相同，十位 1 比 9 小，所以 56 219 较小。
注意：不要只看最后一位，要从左边开始一位一位比。
if the digits are the same, compare the next place = jika sama, banding tempat seterusnya
If the highest digits are the same, move one place to the right and compare again. Keep moving right until you find the first place where the digits are different; that place decides which number is bigger.
Example: 56 219 and 56 291 match in the ten thousands, thousands and hundreds, but in the tens 1 is smaller than 9, so 56 219 is smaller.
Watch out: do not look only at the last digit; start from the left.
Bilangan digit
Nombor empat digit lebih kecil
Melur 9 862
| puluh ribu | ribu | ratus | puluh | sa |
|---|---|---|---|---|
| 9 | 8 | 6 | 2 | |
| 2 | 3 | 8 | 1 | 7 |
9 862 lebih kecil daripada 23 817.
位数不同 = bilangan digit berbeza
四位数的万位是空的，也就是 0。所以任何四位数都比任何五位数小，不必再比其他数位。比较前先数位数，可以省很多时间。
例子：9 999 比 10 000 小，虽然 9 999 的数字看起来都很大。
注意：比较时要把数位对齐，个位对个位，不能左边对齐。
different number of digits = bilangan digit berbeza
A four-digit number has nothing in the ten thousands place, so it is 0 there. That makes every four-digit number smaller than every five-digit number, without comparing the other places. Counting digits first saves time.
Example: 9 999 is smaller than 10 000, even though its digits look big.
Watch out: line the numbers up by the ones place, not by the left edge.
Susun nombor
Tertib menaik dan tertib menurun
Menaik: kecil → besar · Menurun: besar → kecil
Tertib menaik
9 862, 23 817, 31 405, 31 540Tertib menurun
31 540, 31 405, 23 817, 9 862升序 = tertib menaik；降序 = tertib menurun
排列几个数时，先用比较的方法找出最小的数，再找第二小的，依次排下去，就是升序；反过来从最大排到最小，就是降序。降序正好是升序倒过来。
例子：升序 4 500、14 500、41 500；降序 41 500、14 500、4 500。
注意：排好后检查一次，数的个数不能多也不能少。
ascending order = tertib menaik; descending order = tertib menurun
To arrange numbers, compare them to find the smallest, then the next smallest, and so on; that is ascending order. Going from the largest down to the smallest is descending order, which is simply the ascending list reversed.
Example: ascending 4 500, 14 500, 41 500; descending 41 500, 14 500, 4 500.
Watch out: after arranging, check that no number is missing or repeated.
Garis nombor
Nombor di sebelah kanan lebih besar
P 45 480 · Q 45 050 · R 45 900 · S 45 120
45 000
45 500
46 000
P
▼
▼
Q
▼
▼
R
▼
▼
S
▼
▼
Tertib menurun: 45 900, 45 480, 45 120, 45 050
数线 = garis nombor
数线上的数从左到右越来越大。把几个数标在数线上，最右边的就是最大的，最左边的就是最小的。要排降序，就从右往左读；要排升序，就从左往右读。
例子：在 20 000 到 21 000 的数线上，20 900 在 20 100 的右边，所以 20 900 较大。
注意：数线上每一小格代表多少，要先看清楚。
number line = garis nombor
On a number line, numbers get bigger from left to right. When several numbers are marked, the one furthest right is the largest and the one furthest left is the smallest. Read right to left for descending order and left to right for ascending order.
Example: on a line from 20 000 to 21 000, 20 900 is to the right of 20 100, so it is bigger.
Watch out: check how much each small step on the line is worth.
Nombor di antara
Cari nombor di antara dua nombor
52 300 < K < 52 900
52 000
52 500
53 000
52 300
▼
▼
52 900
▼
▼
K boleh jadi 52 400, 52 600, 52 850 …
两数之间 = di antara dua nombor
如果一串数是按升序排的，中间那个位置的数，一定比左边的数大、比右边的数小。可以在数线上把两个数之间的范围标出来，范围里面的数都可以。
例子：17 100 和 17 400 之间的数有 17 250、17 399 等。
注意：刚好等于两端的数不算在中间。
between two numbers = di antara dua nombor
In a list arranged in ascending order, a number in the middle position must be bigger than the one on its left and smaller than the one on its right. Mark the two numbers on a number line; any number in the gap works.
Example: numbers between 17 100 and 17 400 include 17 250 and 17 399.
Watch out: the two end numbers themselves are not between.
Masukkan nombor baharu
Nombor manakah di tengah sekarang?
Susun semula selepas nombor baharu dimasukkan.
Asal (menaik):
51 207, 51 720, 52 017, 52 170
Masukkan 50 972:
50 972, 51 207, 51 720, 52 017, 52 170
5 nombor → nombor ke-3 di tengah
插入新数 = masukkan nombor baharu；中间 = tengah
几个数已经按次序排好，再放进一个新数时，要先把新数和原来的数逐一比较，找到它该站的位置，而不是直接放在最后。排好以后数一数总共有几个数：五个数的时候，排第三位的数就在正中间，左右各有两个数。
例子：18 200、18 900、19 400、19 700 加入 19 050 → 18 200、18 900、19 050、19 400、19 700，中间是 19 050。
注意：插入新数以后，中间的数可能会改变；如果原来的次序是降序，新数也要按降序放。
insert a new number = masukkan nombor baharu; middle = tengah
When a new number joins a list that is already in order, compare it with the numbers in the list to find where it belongs; do not just put it at the end. Then count the numbers. With five numbers, the third one is in the middle, with two on each side.
Example: 18 200, 18 900, 19 400, 19 700 plus 19 050 gives 18 200, 18 900, 19 050, 19 400, 19 700, so the middle is 19 050.
Watch out: after inserting, the middle number may change, and a descending list must stay descending.
Semak cepat
68 245 ___ 68 452
比较两个数 = banding dua nombor
题目要你在两个数之间填上正确的比较词。两个数都是五位数，就从最左边的万位开始比；数字相同就往右移一位，直到遇到最先出现不同的数位，那个数位的数字谁大，整个数就大。
例子：37 610 和 37 160 → 万位、千位相同，百位 6 比 1 大，所以 37 610 较大。
注意：两个数用的数字一样、只是次序不同时，特别容易看错，一定要一位一位对齐比较。
compare two numbers = banding dua nombor
Choose the right words to compare the two numbers. Both have five digits, so start at the ten thousands and move right while the digits are the same. The first place where they differ decides which number is bigger.
Example: 37 610 and 37 160 match in the first two places, and in the hundreds 6 is bigger than 1, so 37 610 is the bigger number.
Watch out: when two numbers use the same digits in a different order, line them up and compare place by place.
Tertib menaik
Pilih susunan dalam tertib menaik.
升序排列 = susun tertib menaik
要找出从小到大排好的那一组。先数每个数有几位，位数少的一定比较小；位数相同的，从万位开始比，相同就往右比下一位。排好以后，再拿每个选项从头到尾核对次序。
例子：6 204、16 024、16 240、60 124 是升序。
注意：升序是从小到大，降序是从大到小，方向不要弄反；位数不同的数要按个位对齐来比。
ascending order = susun tertib menaik
Find the list that goes from smallest to largest. Count the digits first; a number with fewer digits is smaller. For numbers with the same number of digits, compare from the ten thousands and move right when digits match. Then check each option from start to end.
Example: 6 204, 16 024, 16 240, 60 124 is in ascending order.
Watch out: ascending means small to big and descending means big to small; line numbers up by the ones place.
Cari K
74 150, K, 74 900 disusun dalam tertib menaik. Nombor manakah boleh menjadi K?
找中间的数 = cari nombor di tengah
三个数按升序排，K 在中间，所以 K 要同时符合两个条件：比左边的数大，又比右边的数小。逐个选项检查这两个条件，只满足一个条件的都不行。
例子：30 200、K、30 800 是升序，K 可以是 30 500，因为它比 30 200 大、又比 30 800 小。
注意：看起来很接近的数，可能在较高的数位就已经不一样了，要从万位比起。
find the middle number = cari nombor di tengah
The three numbers are in ascending order with K in the middle, so K must be bigger than the left number and smaller than the right number. Test every option against both conditions.
Example: for 30 200, K, 30 800, K could be 30 500 because it is bigger than 30 200 and smaller than 30 800.
Watch out: numbers that look close may already differ in a high place, so compare from the ten thousands.
Tertib menurun
Susun dalam tertib menurun.
降序排列 = susun tertib menurun
要按从大到小的次序点这几个数。先找最大的：位数多的比较大；位数相同就从万位比，相同再往右比。每点一个数，就在剩下的数里再找最大的，一直到最后一个。
例子：降序 52 480、52 408、25 840、5 248。
注意：前几位都相同的两个数，要一直比到出现不同的数位为止，不要只看最后一位。
descending order = susun tertib menurun
Tap the numbers from largest to smallest. Find the largest first: more digits means bigger; with the same number of digits compare from the ten thousands and move right if digits match. After each tap, find the largest of the numbers left.
Example: descending 52 480, 52 408, 25 840, 5 248.
Watch out: when two numbers share their first few digits, keep comparing until a place differs; do not look only at the last digit.
Nombor baharu
Tertib menaik: 36 840, 38 460, 38 604, 38 640. Nombor 38 406 dimasukkan. Nombor manakah di tengah sekarang?
插入新数 = masukkan nombor baharu
原来的四个数已经按升序排好，现在放进一个新数，问哪个数在正中间。做法：先把新数和原来的数逐一比较，找到它的位置，把五个数重新写成一排；五个数的中间是排第三位的数。
例子：18 200、18 900、19 400、19 700 加入 18 150 → 18 150、18 200、18 900、19 400、19 700，中间是 18 900。
注意：新数不一定排在最后；数字很像的数要逐位比较，才能放对位置。
insert a new number = masukkan nombor baharu
Four numbers are in ascending order and one new number joins them; which number is in the middle now? Compare the new number with the list to find its place, rewrite all five in order, and take the third one.
Example: 18 200, 18 900, 19 400, 19 700 plus 18 150 gives 18 150, 18 200, 18 900, 19 400, 19 700, so the middle is 18 900.
Watch out: the new number does not always go at the end; compare similar-looking numbers digit by digit.
Ringkasan
Syabas!
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Banding digit dari tempat paling tinggi. Menaik: kecil ke besar. Menurun: besar ke kecil.
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