Unit 24
Akal Pintar
?38 × 23 = nombor lima digit
Cari digit terkecil yang boleh diisi di tempat ratus.
找最小的百位 = cari digit ratus paling kecil
题目里的三位数只知道十位和个位，百位是空的。要找出百位最少要放几，乘以 23 以后的积才会是五位数，也就是至少 10 000。
例子：□5 × 4 要成为三位数，□ 最小是 2（15 × 4 = 60 不够，25 × 4 = 100 刚好）。
注意：“最小”的意思是：比它小的数字都不行。
find the smallest hundreds digit = cari digit ratus paling kecil
We know only the tens and ones of the three-digit number; the hundreds digit is missing. We need the smallest hundreds digit that makes the product with 23 a five-digit number, which means at least 10 000.
Example: for □5 × 4 to have three digits, the smallest □ is 2 (15 × 4 = 60 is not enough, 25 × 4 = 100 is just enough).
Watch out: smallest means that every smaller digit fails.
Langkah 1
Anggar dahulu
23 × ? ≥ 10 000
23 ≈ 20
20 × 500 = 10 000
→ cuba 338 dan 438
20 × 500 = 10 000
→ cuba 338 dan 438
先估计 = anggar dahulu
23 大约是 20，20 乘 500 刚好一万，所以三位数大约要四五百才够。这样就不用从 0 试到 9，只要试几个接近的数字就好。
例子：要让 □00 × 30 至少一万，30 × 300 = 9 000 不够，30 × 400 = 12 000 就够了。
注意：估计只是缩小范围，最后一定要算准确的积。
estimate first = anggar dahulu
23 is about 20, and 20 × 500 = 10 000, so the three-digit number needs to be around four or five hundred. Instead of trying every digit from 0 to 9, we only test a few close ones.
Example: for □00 × 30 to reach 10 000, 30 × 300 = 9 000 is not enough but 30 × 400 = 12 000 is.
Watch out: estimating only narrows the choices; always work out the exact product at the end.
Langkah 2
Uji dengan darab
338 × 23 dan 438 × 23
✘ 3
| 3 | 3 | 8 | ||
| × | 2 | 3 | ||
| 1 | 0 | 1 | 4 | |
| + | 6 | 7 | 6 | 0 |
| 7 | 7 | 7 | 4 |
✔ 4
| 4 | 3 | 8 | |||
| × | 2 | 3 | |||
| 1 | 3 | 1 | 4 | ||
| + | 8 | 7 | 6 | 0 | |
| 1 | 0 | 0 | 7 | 4 |
验证 = uji
百位放 3：338 × 23 = 7 774，只有四位，不行；百位放 4：438 × 23 = 10 074，是五位数，可以。比 4 小的都不行，所以最小的百位是 4。
例子：若 3 可以，就还要再试 2，确定是不是更小的也行。
注意：只算一个是不够的，要证明比它小的那个不行。
test it = uji
With 3 hundreds: 338 × 23 = 7 774, only four digits, so it fails. With 4 hundreds: 438 × 23 = 10 074, five digits, so it works. Every digit smaller than 4 fails, so the smallest hundreds digit is 4.
Example: if 3 had worked, we would also need to test 2 to see whether an even smaller digit works.
Watch out: finding one that works is not enough; show that the one below it fails.
Cuba
?50 × 40 = nombor lima digit. Digit terkecil di tempat ratus ialah …
试一试 = cuba
先估计：40 要乘几百才会到一万？用估计找出一两个可能的百位数字，再把整个三位数写出来，逐个做乘法。积大于或等于 10 000 就是五位数。找到可以的数字后，还要证明比它小的数字不行。
例子：□00 × 20 要成为五位数，400 × 20 = 8 000 不够，500 × 20 = 10 000 刚好，所以 □ 最小是 5。
注意：每个试的数字都要写成完整的三位数再乘，不能只用百位数字去乘。
try it = cuba
Estimate first: about how many hundreds must 40 be multiplied by to reach ten thousand? Use the estimate to pick one or two possible hundreds digits, write the whole three-digit number and multiply each one. A product of 10 000 or more has five digits. When a digit works, also show that the smaller digits do not.
Example: for □00 × 20 to have five digits, 400 × 20 = 8 000 is not enough and 500 × 20 = 10 000 is just enough, so the smallest □ is 5.
Watch out: write each trial as the whole three-digit number before multiplying; do not multiply the hundreds digit alone.
Ringkasan