﻿[Script Info] Title: [Events] Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text Dialogue: 0,0:00:00.00,0:00:00.55,Default,,0000,0000,0000,,. Dialogue: 0,0:00:00.55,0:00:06.87,Default,,0000,0000,0000,,將7/8寫成小數及百分數 Dialogue: 0,0:00:06.87,0:00:08.62,Default,,0000,0000,0000,,我們會從小數開始，然後我們會發現 Dialogue: 0,0:00:08.62,0:00:12.26,Default,,0000,0000,0000,,其實把小數化為百分數還滿容易的 Dialogue: 0,0:00:12.26,0:00:14.66,Default,,0000,0000,0000,,現在，不論何時你看到這樣的問題 Dialogue: 0,0:00:14.66,0:00:15.51,Default,,0000,0000,0000,,其實有時還滿令人困惑的 Dialogue: 0,0:00:15.51,0:00:18.00,Default,,0000,0000,0000,,這就像，我如何把它變成小數， Dialogue: 0,0:00:18.00,0:00:20.38,Default,,0000,0000,0000,,或一個分母為100的分數，或一個百分數? Dialogue: 0,0:00:20.38,0:00:24.16,Default,,0000,0000,0000,,你總是要記得7/8 Dialogue: 0,0:00:24.16,0:00:25.49,Default,,0000,0000,0000,,是等同於… Dialogue: 0,0:00:25.49,0:00:28.12,Default,,0000,0000,0000,,. Dialogue: 0,0:00:28.12,0:00:33.09,Default,,0000,0000,0000,,等同於7除以8 Dialogue: 0,0:00:33.09,0:00:34.83,Default,,0000,0000,0000,,不是8除以7 Dialogue: 0,0:00:34.83,0:00:37.18,Default,,0000,0000,0000,,7除以8 Dialogue: 0,0:00:37.18,0:00:40.58,Default,,0000,0000,0000,,分子除以分母 Dialogue: 0,0:00:40.58,0:00:42.26,Default,,0000,0000,0000,,好，那我如何將它變為小數呢? Dialogue: 0,0:00:42.26,0:00:45.01,Default,,0000,0000,0000,,我們其實就是做一個長除法問題 Dialogue: 0,0:00:45.01,0:00:48.41,Default,,0000,0000,0000,,但我們即使到小數點後面還要繼續除，也就是我們 Dialogue: 0,0:00:48.41,0:00:50.86,Default,,0000,0000,0000,,不會有餘數，或者要直到數字開始不斷重覆 Dialogue: 0,0:00:50.86,0:00:51.54,Default,,0000,0000,0000,,你會了解我們在說什麼 Dialogue: 0,0:00:51.54,0:00:54.33,Default,,0000,0000,0000,,在這題，我們不會有一直重覆的數字 Dialogue: 0,0:00:54.33,0:00:55.79,Default,,0000,0000,0000,,讓我們來試試吧 Dialogue: 0,0:00:55.79,0:00:57.56,Default,,0000,0000,0000,,所以，它是7除以8 Dialogue: 0,0:00:57.56,0:01:03.07,Default,,0000,0000,0000,,. Dialogue: 0,0:01:03.07,0:01:06.91,Default,,0000,0000,0000,,所以8除7是多少? Dialogue: 0,0:01:06.91,0:01:08.53,Default,,0000,0000,0000,,好，8沒辦法乘以整數接近7 Dialogue: 0,0:01:08.53,0:01:10.25,Default,,0000,0000,0000,,商數是0 Dialogue: 0,0:01:10.25,0:01:12.18,Default,,0000,0000,0000,,事實上，我們因此確定是正確的 Dialogue: 0,0:01:12.18,0:01:14.28,Default,,0000,0000,0000,,讓我們寫上小數點 Dialogue: 0,0:01:14.28,0:01:19.02,Default,,0000,0000,0000,,你可以視這為8除7.000 Dialogue: 0,0:01:19.02,0:01:21.94,Default,,0000,0000,0000,,你可以在後面不斷加上0，直到 Dialogue: 0,0:01:21.94,0:01:23.13,Default,,0000,0000,0000,,你除盡為止 Dialogue: 0,0:01:23.13,0:01:26.97,Default,,0000,0000,0000,,所以我們有小數點在這邊，在7的後面 Dialogue: 0,0:01:26.97,0:01:27.64,Default,,0000,0000,0000,,在上面這邊 Dialogue: 0,0:01:27.64,0:01:30.23,Default,,0000,0000,0000,,所以，8除7等於0乘以 Dialogue: 0,0:01:30.23,0:01:33.09,Default,,0000,0000,0000,,0乘以8等於0 Dialogue: 0,0:01:33.09,0:01:34.41,Default,,0000,0000,0000,,減掉 Dialogue: 0,0:01:34.41,0:01:36.52,Default,,0000,0000,0000,,7減0等於7 Dialogue: 0,0:01:36.52,0:01:38.98,Default,,0000,0000,0000,,現在把0放下來 Dialogue: 0,0:01:38.98,0:01:40.23,Default,,0000,0000,0000,,把一個0放下來 Dialogue: 0,0:01:40.23,0:01:41.57,Default,,0000,0000,0000,,變為70 Dialogue: 0,0:01:41.57,0:01:45.01,Default,,0000,0000,0000,,8除70是多少? Dialogue: 0,0:01:45.01,0:01:47.37,Default,,0000,0000,0000,,8x8=64，這樣行得通 Dialogue: 0,0:01:47.37,0:01:48.95,Default,,0000,0000,0000,,8x9=72 Dialogue: 0,0:01:48.95,0:01:49.98,Default,,0000,0000,0000,,太大了 Dialogue: 0,0:01:49.98,0:01:51.23,Default,,0000,0000,0000,,所以就是8 Dialogue: 0,0:01:51.23,0:01:54.73,Default,,0000,0000,0000,,. Dialogue: 0,0:01:54.73,0:01:57.25,Default,,0000,0000,0000,,8x8=64 Dialogue: 0,0:01:57.25,0:02:03.06,Default,,0000,0000,0000,,減掉，70-64=6 Dialogue: 0,0:02:03.06,0:02:05.08,Default,,0000,0000,0000,,你還是有餘數，所以繼續 Dialogue: 0,0:02:05.08,0:02:07.26,Default,,0000,0000,0000,,把另一個0放下來 Dialogue: 0,0:02:07.26,0:02:11.58,Default,,0000,0000,0000,,所以你把另一個0放下來 Dialogue: 0,0:02:11.58,0:02:13.52,Default,,0000,0000,0000,,然後，8除60是多少 Dialogue: 0,0:02:13.52,0:02:16.48,Default,,0000,0000,0000,,8x8=64，太大了 Dialogue: 0,0:02:16.48,0:02:20.67,Default,,0000,0000,0000,,8x7=56，這行得通 Dialogue: 0,0:02:20.67,0:02:24.68,Default,,0000,0000,0000,,所以就是7 Dialogue: 0,0:02:24.68,0:02:27.80,Default,,0000,0000,0000,,7x8=56 Dialogue: 0,0:02:27.80,0:02:29.01,Default,,0000,0000,0000,,減掉 Dialogue: 0,0:02:29.01,0:02:32.30,Default,,0000,0000,0000,,60-56=4 Dialogue: 0,0:02:32.30,0:02:34.78,Default,,0000,0000,0000,,我們還是有餘數，讓我們繼續 Dialogue: 0,0:02:34.78,0:02:35.97,Default,,0000,0000,0000,,把0放下來 Dialogue: 0,0:02:35.97,0:02:39.21,Default,,0000,0000,0000,,所以，讓我們把0放下來 Dialogue: 0,0:02:39.21,0:02:41.71,Default,,0000,0000,0000,,8除40是多少? Dialogue: 0,0:02:41.71,0:02:45.69,Default,,0000,0000,0000,,好，8x5=40，這剛剛好 Dialogue: 0,0:02:45.69,0:02:47.40,Default,,0000,0000,0000,,所以就是5 Dialogue: 0,0:02:47.40,0:02:50.88,Default,,0000,0000,0000,,5x8=40 Dialogue: 0,0:02:50.88,0:02:51.89,Default,,0000,0000,0000,,減掉 Dialogue: 0,0:02:51.89,0:02:53.20,Default,,0000,0000,0000,,沒有餘數 Dialogue: 0,0:02:53.20,0:02:56.45,Default,,0000,0000,0000,,所以關於小數，我們剛算出來7/8 Dialogue: 0,0:02:56.45,0:03:04.82,Default,,0000,0000,0000,,等於7除以8，就等於0.875 Dialogue: 0,0:03:04.82,0:03:11.39,Default,,0000,0000,0000,,所以7/8寫成小數是0.875 Dialogue: 0,0:03:11.39,0:03:13.49,Default,,0000,0000,0000,,現在我們做完了小數的部分 Dialogue: 0,0:03:13.49,0:03:15.20,Default,,0000,0000,0000,,下一個是要做百分數 Dialogue: 0,0:03:15.20,0:03:17.52,Default,,0000,0000,0000,,如果你已經有小數了，要做百分數就 Dialogue: 0,0:03:17.52,0:03:19.16,Default,,0000,0000,0000,,很容易 Dialogue: 0,0:03:19.16,0:03:22.44,Default,,0000,0000,0000,,你只要將小數點往右移兩位 Dialogue: 0,0:03:22.44,0:03:24.28,Default,,0000,0000,0000,,然後放一個百分比符號 Dialogue: 0,0:03:24.28,0:03:25.93,Default,,0000,0000,0000,,我想為什麼這行得通是很合理的 Dialogue: 0,0:03:25.93,0:03:28.52,Default,,0000,0000,0000,,現在你會說，每100有多少? Dialogue: 0,0:03:28.52,0:03:33.60,Default,,0000,0000,0000,,你可以把這視為千分之875 Dialogue: 0,0:03:33.60,0:03:34.43,Default,,0000,0000,0000,,讓我把這寫下來 Dialogue: 0,0:03:34.43,0:03:35.80,Default,,0000,0000,0000,,你可以將這視為分數 Dialogue: 0,0:03:35.80,0:03:41.05,Default,,0000,0000,0000,,你可以說，好，這等於875/1000 Dialogue: 0,0:03:41.05,0:03:42.62,Default,,0000,0000,0000,,這是我們以前學的。這是 Dialogue: 0,0:03:42.62,0:03:45.95,Default,,0000,0000,0000,,千分位 Dialogue: 0,0:03:45.95,0:03:53.34,Default,,0000,0000,0000,,或者你可以將它寫做87.5/100 Dialogue: 0,0:03:53.34,0:03:56.57,Default,,0000,0000,0000,,如果你只移小數點兩位，它是87.5/100 Dialogue: 0,0:03:56.57,0:03:59.06,Default,,0000,0000,0000,,或者如果你只有這個，然後把分子、分母同除以10 Dialogue: 0,0:03:59.06,0:04:01.17,Default,,0000,0000,0000,,你會得到這個 Dialogue: 0,0:04:01.17,0:04:06.70,Default,,0000,0000,0000,,這基本上就是每100有87.5，所以 Dialogue: 0,0:04:06.70,0:04:12.20,Default,,0000,0000,0000,,第二個答案在這邊，這就是說每100有87.5 Dialogue: 0,0:04:12.20,0:04:15.56,Default,,0000,0000,0000,,或者百分比 Dialogue: 0,0:04:15.56,0:04:21.44,Default,,0000,0000,0000,,所以這就等於87.5% Dialogue: 0,0:04:21.44,0:04:23.56,Default,,0000,0000,0000,,所以這給了你為什麼行得通的理由 Dialogue: 0,0:04:23.56,0:04:26.30,Default,,0000,0000,0000,,但真的簡單的方式，如果你有小數要變為百分數 Dialogue: 0,0:04:26.30,0:04:30.71,Default,,0000,0000,0000,,你把它乘以100 Dialogue: 0,0:04:30.71,0:04:32.82,Default,,0000,0000,0000,,然後放一個%在後面，基本上就是除以100 Dialogue: 0,0:04:32.82,0:04:35.09,Default,,0000,0000,0000,,所以你乘以又除以 Dialogue: 0,0:04:35.09,0:04:36.04,Default,,0000,0000,0000,,100 Dialogue: 0,0:04:36.04,0:04:39.46,Default,,0000,0000,0000,,如果你將這乘以100，就等於 Dialogue: 0,0:04:39.46,0:04:42.52,Default,,0000,0000,0000,,把小數點往右移兩位 Dialogue: 0,0:04:42.52,0:04:47.57,Default,,0000,0000,0000,,就變為87.5 Dialogue: 0,0:04:47.57,0:04:48.63,Default,,0000,0000,0000,,然後你想要放上% Dialogue: 0,0:04:48.63,0:04:51.31,Default,,0000,0000,0000,,這會變為百分之… Dialogue: 0,0:04:51.31,0:04:53.36,Default,,0000,0000,0000,,所以你乘以100，然後又除以100 Dialogue: 0,0:04:53.36,0:04:55.51,Default,,0000,0000,0000,,你並沒有改變這個數字 Dialogue: 0,0:04:55.51,0:04:57.01,Default,,0000,0000,0000,,希望，你能理解這道理 Dialogue: 0,0:04:57.01,0:04:58.82,Default,,0000,0000,0000,,另一個記憶的方式，因為有時你可能會困惑 Dialogue: 0,0:04:58.82,0:05:02.28,Default,,0000,0000,0000,,我要把小數點往右嗎? Dialogue: 0,0:05:02.28,0:05:04.55,Default,,0000,0000,0000,,還是往左? 小數點的數字 Dialogue: 0,0:05:04.55,0:05:07.89,Default,,0000,0000,0000,,總是會比百分數的數字部分 Dialogue: 0,0:05:07.89,0:05:08.94,Default,,0000,0000,0000,,來得小 Dialogue: 0,0:05:08.94,0:05:10.82,Default,,0000,0000,0000,,不但比較小，而且 Dialogue: 0,0:05:10.82,0:05:15.06,Default,,0000,0000,0000,,剛好會差100倍 Dialogue: 0,0:05:15.06,0:05:17.87,Default,,0000,0000,0000,,剛好會比87.5 Dialogue: 0,0:05:17.87,0:05:19.91,Default,,0000,0000,0000,,小100倍 Dialogue: 0,0:05:19.91,0:05:21.98,Default,,0000,0000,0000,,很明顯地，當你寫下%，這些就會變成 Dialogue: 0,0:05:21.98,0:05:24.39,Default,,0000,0000,0000,,一樣大 Dialogue: 0,0:05:24.39,0:05:24.60,Default,,0000,0000,0000,,.