Course: 11.9 小数、小数和百分数的写作和比较概率

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将概率与分数、十进制和百分数比较

A spinner is divided into four sections: green, blue, red and yellow. What is the probability of spinning the arrow and having it land in the green section? Write this probability as a fraction, decimal and as a percent.
::旋转器可分为四个部分: 绿色、蓝色、红色和黄色。旋转箭头并将其降落在绿色部分的概率是多少? 将此概率写成小数、小数和百分比。

In this concept, you will learn to write probabilities as fractions, decimals and percent.
::在此概念中,您将学习以分数、小数和百分比来写出概率。

Probabilities as Fractions, Decimals and Percents
::小数、小数和百分数的概率

Probabilities can be computed in terms of ratios. Since any ratio can be turned into a fraction, decimal, or percent, you can also turn any probability into a fraction, decimal, or percent.
::概率可以按比率计算。由于任何比率可以转换成分数、小数或百分比,您也可以将任何概率转换成分数、小数或百分比。

For instance, when you toss a number cube, the probability of rolling a “3” is:
::例如,抛掷数字立方体时,滚动“3”的概率是:

\begin{aligned} \begin{array}{rcl} P (3) & = & favorable outcomes : total outcomes \\ P (3) & = & 1 : 6 \end{array} \end{aligned}

$\begin{align*}\begin{array}{rcl} P(3) &=& \text{favorable outcomes} : \text{total outcomes} \\ P(3) &=& 1 : 6 \end{array}\end{align*}$
::P(3)=有利结果:结果总数P(3)=1:6

The same probability can be written as a fraction simply by rewriting the two numbers in the ratio as the numerator and denominator of a fraction.
::仅通过将两个数字与分数的分子数和分母重写,即可将这两个数字与分数的分子数和分母重写成一个分数。

\begin{aligned} P (3) = \frac{1}{6} \end{aligned}

$\begin{align*}P(3) = \frac{1}{6}\end{align*}$
::P(3)=16

This is the answer in fraction form.
::这是分数形式的答案。

How can this fraction be expressed as a decimal?
::如何用小数点表示这个分数?

The fraction can be expressed as a decimal by dividing the numerator by the denominator.
::分数可以用分母除以分母来表示小数。

\begin{aligned} \frac{1}{6} = & \overset{0.1666}{6 \bar{) 1.0000}} \end{aligned}

$\begin{align*}\frac{1}{6} = & \overset{ \ \ 0.1666}{6 \overline{ ) {1.0000 \;}}}\end{align*}$

The answer is 0.1666… or 0.167.
::答案是0.1666 或0.167

How can this decimal be expressed as a percent?
::如何用百分比表示这个小数点?

The decimal can be expressed as a percent by multiply the decimal by 100 since a percent is out of 100. Then, move the decimal point two places to the right to show the percent.
::小数点可以以百分比表示,乘以小数点乘以100,因为百分率超过100。然后,将小数点两点移到显示百分率的右方。

\begin{aligned} \begin{array}{rcl} % & = & 0.167 \times 100 \\ % & = & 16.7 \end{array} \end{aligned}

$\begin{align*}\begin{array}{rcl} \% &=& 0.167 \times 100 \\ \% &=& 16.7 \end{array}\end{align*}$

The answer is 16.7%.
::答案是16.7%。

The decimal 0.167 is equal to 16.7%.
::小数点0.167等于16.7%。

To summarize, the probability of rolling a 3 with a number cube is 1 out of 6 and can be expressed in the following forms.
::概括地说,以数字立方体滚动一个3的概率是每6个中就有1个,可以以下列形式表示。

Ratio	1:6
Fraction	$\begin{align}\frac{1}{6}\end{align}$
Decimal	0.167
Percent	16.7%

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about your spinner with the four colors. You have a spinner with the colors green, blue, red and yellow. You want to determine the probability of landing on green expressed as a fraction, a decimal, and a percent.
::早些时候, 您被给出了四色的旋转器问题。您有一个绿色、蓝色、红色和黄色的旋转器。您想要确定在绿色上着陆的概率, 以小数、小数和百分比表示。

First, write the fraction.
::首先,写分数。

Green is one out of four colors. Therefore the fraction is:
::绿色是四种颜色中的一种。因此分数是:

\begin{aligned} \frac{1}{4} \end{aligned}

$\begin{align*}\frac{1}{4}\end{align*}$

Next, write the decimal.
::下一位,写小数点

\begin{aligned} \frac{1}{4} = & \overset{0.25}{4 \bar{) 1.00}} \end{aligned}

$\begin{align*}\frac{1}{4} = & \overset{ \ \ 0.25}{4 \overline{ ) {1.00 \;}}}\end{align*}$

Then, write the percent.
::然后,写百分比。

\begin{aligned} \begin{array}{rcl} % & = & 0.25 \times 100 \\ % & = & 25 \end{array} \end{aligned}

$\begin{align*}\begin{array}{rcl} \% &=& 0.25 \times 100 \\ \% &=& 25 \end{array}\end{align*}$

The answers are

\begin{aligned} \frac{1}{4}, 0.25 \end{aligned}

$\begin{align*}\frac{1}{4}, 0.25\end{align*}$ and

\begin{aligned} 25 % \end{aligned}

$\begin{align*}25 \%\end{align*}$ .

The probability of spinning the spinner and landing on green is $\begin{align*}\frac{1}{4}\end{align*}$ or $\begin{align*}0.25\end{align*}$ or $\begin{align*} 25 \%\end{align*}$ .
::旋转旋转器和在绿色上着陆的概率为14或0.25或25%。

Example 2
::例2

Kelly is playing a game at a carnival. She threw four out of 9 rings onto pins. If you write this as a fraction you get $\begin{align*}\frac{4}{9}\end{align*}$ .
::Kelly在嘉年华会上玩游戏,她把9个环中的4个扔到针上。如果你把它写成一个分数,你就会得到49个。

What is it as a decimal or as a percent?
::什么是十进制还是百分数?

First, divide 4 by 9 to create a decimal.
::首先,将4除以9以创建小数点。

\begin{aligned} \frac{4}{9} = & \overset{0.4444}{9 \bar{) 4.0000}} \end{aligned}

$\begin{align*}\frac{4}{9} = & \overset{ \ \ 0.4444}{9 \overline{ ) {4.0000 \;}}}\end{align*}$

The answer is 0.4444… or 0.44.
::答案是0.4444... 或0.44

Next, change the decimal to a percent.
::接下来,将小数点修改为百分之一。

\begin{aligned} \begin{array}{rcl} % & = & 0.44 \times 100 \\ % & = & 44 \end{array} \end{aligned}

$\begin{align*}\begin{array}{rcl} \% &=& 0.44 \times 100 \\ \% &=& 44 \end{array} \end{align*}$

The answer is 44%.
::答案是44%。

The decimal 0.44 is equal to 44%.
::小数点0.44等于44%。

Kelly’s probability is about 44% or she hits the pins 44% of the time. The word “about” is used because the answer was rounded from the decimal to the percent.
::Kelly的概率约为44%左右,或者她到了44%的时间。使用“接近”一词是因为答案从小数点到百分比四舍五入。

Example 3
::例3

Write two out of five in fraction form.
::5个中写2个成分数形式。

Two out of five $\begin{align*}= \frac{2}{5}\end{align*}$
::5个中2个=25

Example 4
::例4

Write two out of five in decimal form.
::以小数数形式写出五分之二。

\begin{aligned} \frac{2}{5} = & \overset{0.4}{5 \bar{) 2.0}} \end{aligned}

$\begin{align*}\frac{2}{5} = & \overset{ \ \ 0.4}{5 \overline{ ) {2.0 \;}}}\end{align*}$

The answer is 0.4.
::答案是0.4

Example 5
::例5

Write two out of five in percent form.
::以百分比形式写出五分之二

\begin{aligned} \begin{array}{rcl} % & = & 0.4 \times 100 \\ % & = & 40 \end{array} \end{aligned}

$\begin{align*}\begin{array}{rcl} \% &=& 0.4 \times 100 \\ \% &=& 40 \end{array}\end{align*}$

The answer is 40%.
::答案是40%。

Review
::回顾

Answer the questions below.
::回答下列问题。

A bag has 6 red marbles, 5 blue marbles, 7 green marbles, 2 white marbles, and 5 yellow marbles. Find the probability of randomly picking out one of the following.
::袋子里有6个红色大理石、5个蓝色大理石、7个绿色大理石、2个白色大理石和5个黄色大理石。找到随机挑选以下部分之一的可能性。

What is the probability in fraction form of choosing red marble?
::选择红大理石的几分数概率是多少?

What is the probability in decimal form of choosing red marble?
::选择红大理石的十进制概率是多少?

What is the probability of choosing red marble as a percent?
::选择红大理石作为百分比的概率是多少?

What is the probability in fraction form of choosing blue marble?
::选择蓝色大理石的概率是多少?

What is the probability in decimal form of choosing blue marble?
::选择蓝色大理石的几率以小数表示是多少?

What is the probability of choosing blue marble as a percent?
::选择蓝色大理石作为百分比的概率是多少?

What is the probability in fraction form of choosing green marble?
::选择绿色大理石的几分数概率是多少?

What is the probability in fraction form of choosing white marble?
::选择白大理石的几分数概率是多少?

What is the probability in decimal form of choosing green marble?
::选择绿色大理石的几率以小数表示是多少?

What is the probability in percent form of choosing a green or blue marble?
::选择绿色或蓝色大理石的概率(百分率)是多少?

What is the probability in fraction form of choosing yellow marble?
::选择黄色大理石的几分数概率是多少?

What is the probability in decimal form of choosing yellow marble?
::选择黄色大理石的几率以小数表示是多少?

What is the probability of choosing yellow marble as a percent?
::选择黄色大理石作为百分比的概率是多少?

Which 3 marbles together have a 60 percent chance of being chosen?
::三个大理石共有60% 被选中的几率?

Which 2 marbles together have a 48 percent chance of being chosen?
::两颗大理石共有48% 被选中的可能性?

Which 3 marbles together have a 0.72 chance of being chosen?
::三个大理石共有0.72个被选中的机会?

Review (Answers)
::回顾(答复)

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。

Section outline

General

将概率与分数、十进制和百分数比较

Probabilities as Fractions, Decimals and Percents ::小数、小数和百分数的概率

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Example 5 ::例5

Review ::回顾

Review (Answers) ::回顾(答复)

Resources ::资源