4.12十进制四舍五入和除法

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• 选择节十进制四舍五入和除法

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  十进制四舍五入和除法

  

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  Vincent is looking at a cupcake recipe. The recipe makes a dozen cupcakes, but he only wants to make 4 cupcakes. He knows that 4 out of 12 is also one-third. If he divides the ingredients in the recipe by 3, he will have enough ingredients to make just 4 cupcakes. The recipe calls for 215 grams of sugar and his kitchen scale only measures grams to the tenths place. How much sugar should Vincent measure out to make a third of the recipe?
  ::文森特正在看一个蛋糕配方。 配方做了十几个蛋糕, 但他只想做4个蛋糕。 他知道12个中就有4个也是三分之一。 如果他把配方的配方除以3, 他就会有足够的配方来做4个蛋糕。 配方需要215克的糖, 而他的厨房规模只相当于10岁。 文森特应该用多少糖来做配方的三分之一?

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  In this concept, you will learn to  divide  and  round  decimals.
  ::在此概念中,您将学会将小数点和小数点舍入到四舍五入。

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  Rounding Decimals When Dividing
  ::分决时的十进制四进制四舍四舍五入

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  You can divide decimals by  whole numbers  and use  zero  placeholders  to find the most accurate  quotient . Some quotients are so long that it is difficult to decipher the value of the decimal.  Rounding  the decimal number to a decimal  place value  would make the number easier to evaluate.
  ::您可以将小数点除以整数, 并使用零占位符来找到最准确的商数。 有些商数太长, 很难破解小数点的值。 将小数点四舍五入到小数点的位数值会使数字更容易评估 。

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  Remember to look at the number to the right of the place value you are rounding to. If the number is less than 5, round the number down. If the number is equal to or greater than 5, round the number up.
  ::记住要查看您正在四舍五入的位置值右侧的数值。 如果数字小于5, 则将数字下转。 如果数字等于或大于5, 则将数字上转。

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  Round 2.1046891425 to the nearest hundredths place. The number to the right of the hundredths place is 4. Round the number down.
  ::2.104681425回合至最近的第一百个位。第一百个位右侧的数是4, 将数字四舍五入。

  $$\begin{array}{r}\begin{array}{rcl}& & 2.1\underset{\_}{0}46891425\approx 2.10\\ & & \uparrow \end{array}\end{array}$$

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  Round 2.1046891425 to the nearest ten-thousandths place. The number to the right of the ten-thousandths place is 8. Round the number up.
  ::圆21046891425到最近的十千米处。十千米处右边的号码是八。

  $$\begin{array}{r}\begin{array}{rcl}& & 2.104\underset{\_}{6}891425\approx 2.1047\\ & & \uparrow \end{array}\end{array}$$

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  Here is a   problem. Round the quotient to the nearest ten-thousandths place.
  ::有个问题,把商数绕到最近的十千个地方

  $$\begin{array}{r}1.265÷4\end{array}$$

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  First, divide to find the quotient. Remember to bring up the  decimal point  in the same location as the  dividend .
  ::首先, 分裂以找到商数 。 记住在与股息相同的地点上调小数点 。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{0.31625}{4\overline{)1.26500}}\\ & & \underset{\_}{-12}\\ & & 06\\ & & \underset{\_}{-4}\\ & & 25\\ & & \underset{\_}{-24}\\ & & 10\\ & & \underset{\_}{-8}\\ & & 20\\ & & \underset{\_}{-20}\\ & & 0\end{array}\end{array}$$

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  Then, take the quotient and round it to the nearest ten-thousandths place. Look at the digit to the right of the ten-thousandths; it is 5. Round the number up.
  ::然后,将商数绕到最近的十千个点。看看十千个点右边的位数,是五。

  $$\begin{array}{r}\begin{array}{rcl}& & 0.316\underset{\_}{2}5\approx 0.3163\\ & & \uparrow \end{array}\end{array}$$

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  The quotient of 1.265 divided by 4 rounded to the nearest ten-thousandths place is 0.3163.
  ::1.265的商数除以4,四舍五入至最近的十千位,即0.3163。

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  Keep in mind some decimal quotients can be quite long.
  ::记住一些小数位数可能很长。

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  Here is a division problem with a very long quotient. Round the quotient to thousandths.
  ::这是一个分裂问题,其商数非常长。将商数四舍五入到千位。

  $$\begin{array}{r}\begin{array}{rcl}& & 13.87÷7=1.9814285714285713\\ & & 1.98\underset{\_}{1}4285714285713\approx 1.981\\ & & \uparrow \end{array}\end{array}$$

   

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  The quotient of 13.87 divided by 7, rounded to the thousandths is 1.981
  ::以13.87除以7除以7,四舍五入至千位的商数为1.981

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  If you know you will round the quotient, you can stop dividing after you’ve found the digit to the right of the place value you are rounding to. Take for example the problem above. Stop dividing once you’ve found the digit in the ten-thousandths place. The digits that come afterwards will not affect the rounding of the decimal number.
  ::如果您知道您将绕过商数, 您可以在您找到您正在舍入的位数右侧的位数后停止分割 。 例如上面的问题 。 一旦您在十千个位数中找到了位数, 停止分割 。 之后出现的位数不会影响小数点的四舍五入 。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{1.98\underset{\_}{1}4}{7\overline{)13.8700}}\\ & & \underset{\_}{-7}\\ & & 68\\ & & \underset{\_}{-63}\\ & & 57\\ & & \underset{\_}{-56}\\ & & 10\\ & & \underset{\_}{-7}\\ & & 30\\ & & \underset{\_}{-28}\\ & & 2\end{array}\end{array}$$

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  Round 1.9814 to the thousandths place.
  ::1.9814回合到一千个地方

  $$\begin{array}{r}\begin{array}{rcl}& & 1.98\underset{\_}{1}4\approx 1.981\\ & & \uparrow \end{array}\end{array}$$

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  The answer is the same, 1.981.
  ::答案是一样的,1.981

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about Vincent making cupcakes.
  ::之前有人给你一个 文森特做蛋糕的问题

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  He is trying to make a third of a cupcake recipe by dividing the ingredients by 3. Since his kitchen scale only measures to a tenths of a gram, find a third of 215 grams of sugar, rounded to the tenths place.
  ::他试图通过将配料除以3 来做出三分之一的蛋糕配方,因为他的厨房规模只测量到十分之一的一克,发现糖的三分之一是215克,四舍五入到十分之一。

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  First, divide to find the quotient. You can stop at the hundredths place.
  ::首先,分头寻找商数。你可以停在第一百个地方。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{71.\underset{\_}{6}6}{3\overline{)215.00}}\\ & & \underset{\_}{-21}\\ & & 05\\ & & \underset{\_}{-3}\\ & & 20\\ & & \underset{\_}{-18}\\ & & 20\\ & & \underset{\_}{-18}\\ & & 2\end{array}\end{array}$$

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  Then, round the quotient to the tenths place.
  ::然后,将商数绕到十分位。

  $$\begin{array}{r}\begin{array}{rcl}& & 71.\underset{\_}{6}6\approx 71.7\\ & & \uparrow \end{array}\end{array}$$

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  Example 2
  ::例2

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  Find the quotient and round it to the nearest thousandth.
  ::找到商数,绕到最近的千位

  $$\begin{array}{r}0.45622÷4\end{array}$$

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  First, divide to find the quotient. Add zero placeholders if necessary. Remember to bring up the decimal point in the same location as the dividend. Divide all the way or you can stop dividing once you’ve found the digit in the ten-thousandths place.
  ::首先,为找到商数而划分。 如果需要, 添加零占位符。 记住在与股息相同的地点上调小数点。 全部分割或者一旦在千位位数中找到数字, 就可以停止分割 。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{0.114055}{4\overline{)0.456220}}\\ & & \underset{\_}{-4}\\ & & 05\\ & & \underset{\_}{-4}\\ & & 16\\ & & \underset{\_}{-16}\\ & & 02\\ & & \underset{\_}{-0}\\ & & 22\\ & & \underset{\_}{-20}\\ & & 20\\ & & \underset{\_}{-20}\\ & & 0\end{array}\end{array}$$

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  OR
  ::或

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{0.1140}{4\overline{)0.45622}}\\ & & \underset{\_}{-4}\\ & & 05\\ & & \underset{\_}{-4}\\ & & 16\\ & & \underset{\_}{-16}\\ & & 02\\ & & \underset{\_}{-0}\\ & & 2\end{array}\end{array}$$

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  Then, round the quotient to the thousandths place. Look at the digit to the right in the ten-thousandths place; it is 0. Round the number down.
  ::然后,将商数绕到千位。看看十千位的右位数字,是0。把数字按下。

  $$\begin{array}{r}\begin{array}{rcl}& & 0.11\underset{\_}{4}055\approx 0.114\text{OR}0.11\underset{\_}{4}0\approx 0.114\\ & & \uparrow \uparrow \end{array}\end{array}$$

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  The quotient of 0.45622 divided by 4 rounded to the thousandths place is 0.114. Both methods will bring you to the same conclusion. The method on the right may be quicker if you only need a rounded quotient.
  ::0.45622 的商数除以 4 四舍五入到千位是 0.14。 两种方法都会使您得出相同的结论。 右侧的方法可能更快, 如果您只需要四舍五入的商数 。

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  Find the quotient rounded to the nearest thousandths for the following problems.
  ::查找以下各问题的四舍五入至千位的商数。

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  Example 3
  ::例3

  $$\begin{array}{r}0.51296÷2=\underset{\_}{}\end{array}$$

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  First, divide to find the quotient.
  ::首先,分化寻找商数。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{0.25648}{2\overline{)0.51296}}\\ & & \underset{\_}{-4}\\ & & 11\\ & & \underset{\_}{-10}\\ & & 12\\ & & \underset{\_}{-12}\\ & & 09\\ & & \underset{\_}{-8}\\ & & 16\\ & & \underset{\_}{-16}\\ & & 0\end{array}\end{array}$$

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  Then, round the quotient to the thousandths place.
  ::然后,绕着商数到一千个地方

  $$\begin{array}{r}\begin{array}{rcl}& & 0.25\underset{\_}{6}48\approx 0.256\\ & & \uparrow \end{array}\end{array}$$

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  The quotient of 0.51296 divided by 2 is 0.256.
  ::0.51296除以2的商数为0.256。

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  Example 4
  ::例4

  $$\begin{array}{r}10.0767÷3=\underset{\_}{}\end{array}$$

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  First, divide to find the quotient.
  ::首先,分化寻找商数。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{3.3589}{3\overline{)10.0767}}\\ & & \underset{\_}{-9}\\ & & 10\\ & & \underset{\_}{-9}\\ & & 17\\ & & \underset{\_}{-15}\\ & & 26\\ & & \underset{\_}{-24}\\ & & 27\\ & & \underset{\_}{-27}\\ & & 0\end{array}\end{array}$$

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  Then, round the quotient to the thousandths place.
  ::然后,绕着商数到一千个地方

  $$\begin{array}{r}\begin{array}{rcl}& & 3.35\underset{\_}{8}9\approx 3.359\\ & & \uparrow \end{array}\end{array}$$

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  The quotient of 10.0767 divided by 3 is 3.359.
  ::10.0767除以3的商数为3.359。

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  Example 5
  ::例5

  $$\begin{array}{r}0.48684÷2=\underset{\_}{}\end{array}$$

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  First, divide to find the quotient. You can stop at the ten-thousandths place.
  ::首先,分头寻找商数。你可以停在10千个地方。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{0.24\underset{\_}{3}4}{2\overline{)0.48684}}\\ & & \underset{\_}{-4}\\ & & 08\\ & & \underset{\_}{-8}\\ & & 06\\ & & \underset{\_}{-6}\\ & & 08\\ & & \underset{\_}{-8}\\ & & 04\end{array}\end{array}$$

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  Then, round the quotient to the thousandths place.
  ::然后,绕着商数到一千个地方

  $$\begin{array}{r}\begin{array}{rcl}& & 0.24\underset{\_}{3}4\approx 0.243\\ & & \uparrow \end{array}\end{array}$$

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  The quotient of 0.48684 divided by 2 rounded to the thousandths is 0.243.
  ::0.48684除以2四舍五入至千分之0.243的商数。

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  Review
  ::回顾

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  Find each quotient rounded to the nearest thousandths.
  ::查找每个四舍五入到千位的商数。

  1. $\begin{array}{r}0.54686÷2\end{array}$
  2. $\begin{array}{r}0.84684÷2\end{array}$
  3. $\begin{array}{r}0.154586÷2\end{array}$  
  4. $\begin{array}{r}0.34689÷3\end{array}$
  5. $\begin{array}{r}0.994683÷3\end{array}$
  6. $\begin{array}{r}0.154685÷5\end{array}$
  7. $\begin{array}{r}0.546860÷5\end{array}$
  8. $\begin{array}{r}0.25465÷5\end{array}$
  9. $\begin{array}{r}0.789003÷3\end{array}$
  10. $\begin{array}{r}0.18905÷5\end{array}$
  11. $\begin{array}{r}0.27799÷9\end{array}$
  12. $\begin{array}{r}0.354680÷10\end{array}$
  13. $\begin{array}{r}0.454686÷6\end{array}$
  14. $\begin{array}{r}0.954542÷2\end{array}$
  15. $\begin{array}{r}0.8546812÷4\end{array}$

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  Review (Answers) 
  ::回顾(答复)

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  Click   to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

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  Resources
  ::资源