📚 Year 8 Higher Unit 3: Place Value, Ordering and Rounding | 八年级高阶第三单元：位值、排序与四舍五入
Welcome to this Unit 3 revision guide. It covers the core number skills you need for Year 8 Higher: reading decimal place values, multiplying and dividing by 10, 100 and 1000, comparing and rounding decimals, using significant figures, and working with upper and lower bounds. These skills underpin measurement, estimation, data handling and many algebra topics.
欢迎使用本单元复习指南。它涵盖八年级高阶第三单元的核心数字技能：读取小数位值、乘除以10、100和1000、比较和四舍五入小数、使用有效数字，以及计算上界与下界。这些技能是测量、估算、数据处理和许多代数主题的基础。
1. Place Value and the Decimal System | 位值与十进制系统
In our base-10 system, the value of a digit depends entirely on its position. Moving one place to the left multiplies the value by 10; moving one place to the right divides it by 10. For example, in 482.57 the 4 means 400, the 8 means 80, the 2 means 2, the 5 means 5/10 and the 7 means 7/100.
在十进制中，数字的值完全取决于它所在的位置。向左移动一位乘以10，向右移动一位除以10。例如在482.57中，4表示400，8表示80，2表示2，5表示5/10，7表示7/100。
You can expand any decimal using place-value columns: hundreds, tens, units, tenths, hundredths and thousandths. This expanded form makes it much easier to compare, add, subtract, multiply and divide decimals accurately.
你可以用位值列展开任何小数：百位、十位、个位、十分位、百分位和千分位。这种展开形式使小数的比较、加减乘除更加准确。
482.57 = 4×100 + 8×10 + 2×1 + 5×(1/10) + 7×(1/100)
2. Multiplying and Dividing by Powers of 10 | 乘除以10的幂
To multiply a decimal by 10, move every digit one place to the left; by 100, move two places; by 1000, move three places. To divide, move the digits to the right. This works because multiplying by 10 makes each place value ten times larger, while dividing makes it ten times smaller.
小数乘以10时，每个数字向左移动一位；乘以100，移动两位；乘以1000，移动三位。除以时向右移动。这是因为乘以10使每个位值变大十倍，除以10使每个位值变小十倍。
e that dividing by 100 is the same as multiplying by 1/100, so the decimal point effectively moves left.
例如，3.25 × 100 = 325，因为两个数字都向左移动两位。同样，57 ÷ 10 = 5.7，0.08 × 1000 = 80。注意除以100等于乘以1/100，因此小数点向左移动。
3.25 × 100 = 325, 57 ÷ 10 = 5.7, 0.08 × 1000 = 80
3. Comparing and Ordering Decimals | 比较和排序小数
To compare decimals, write them with the same number of decimal places by adding trailing zeros, then compare column by column from left to right. This prevents the common mistake of thinking that 0.56 is greater than 0.6 because 56 is greater than 6.
比较小数时，先通过补零使它们小数位数相同，然后从左到右逐位比较。这可以避免因为56大于6就误以为0.56大于0.6的常见错误。
For example, compare 0.6, 0.56 and 0.605. Write them as 0.600, 0.560 and 0.605. Comparing the tenths column shows that 0.560 has 5 tenths while the others have 6 tenths, so 0.56 is smallest. Then compare hundredths: 0.600 has 0, while 0.605 has 5, so the order is 0.56 < 0.6 < 0.605.
例如，比较0.6、0.56和0.605。把它们写成0.600、0.560和0.605。比较十分位可知0.560有5个十分位，而其他两个有6个十分位，因此0.56最小。再比较百分位：0.600有0，0.605有5，所以顺序为0.56 < 0.6 < 0.605。
On a number line, decimals are ordered according to their distance from zero. The smallest number is furthest left, and the largest is furthest right. Ordering skills are tested frequently in questions on measurements, temperatures and data.
在数轴上，小数按它们与零的距离排序。最小的数在最左边，最大的数在最右边。排序技能在测量、温度和数据题中经常考查。
4. Adding and Subtracting Decimals | 小数的加减法
When adding or subtracting decimals, align the decimal points vertically and fill empty places with zeros. Then add or subtract each column as usual. Keeping the decimal points in a straight line ensures that tenths are added to tenths, hundredths to hundredths, and so on.
加减小数时，竖直对齐小数点，并在空位补零。然后像往常一样逐位加减。保持小数点成一条直线可以确保十分位加十分位、百分位加百分位。
ow carefully when needed: 10.0 - 3.27 = 6.73. Always check by estimating the answer first.
例如：12.7 + 3.45 = 16.15，因为12.70 + 3.45 = 16.15。减法时注意借位：10.0 - 3.27 = 6.73。做题前先估算检验结果。
12.70 + 3.45 = 16.15, 10.0 - 3.27 = 6.73
5. Multiplying Decimals | 小数乘法
To multiply decimals, first ignore the decimal points and multiply the numbers as whole numbers. Then count the total number of decimal places in both original factors and put the decimal point back into the product so it has that many decimal places.
小数相乘时，先忽略小数点，把数当作整数相乘。然后数出两个因数的小数位总数，在乘积中点上小数点，使小数位数与总数相同。
nd there are two decimal places in total, so the product is 4.20, which is written as 4.2.
例如0.4 × 0.6：4 × 6 = 24，共有两位小数，所以0.4 × 0.6 = 0.24。1.2 × 3.5：12 × 35 = 420，共有两位小数，所以乘积是4.20，写作4.2。
1.2 × 3.5 = (12 ÷ 10) × (35 ÷ 10) = 420 ÷ 100 = 4.2
6. Dividing Decimals | 小数除法
If the divisor is a decimal, multiply both the divisor and the dividend by 10, 100 or 1000 until the divisor becomes a whole number. Then perform normal long division. This does not change the value of the quotient because you are multiplying by 1 in the form of 10/10, 100/100 or 1000/1000.
如果除数是小数，把除数和被除数同时乘以10、100或1000，直到除数变成整数。然后进行普通的除法。这不会改变商的值，因为你相当于乘以10/10、100/100或1000/1000，即乘以1。
When the answer is not exact, you may need to give it to a specified number of decimal places or significant figures.
例如：4.8 ÷ 0.6 等于 48 ÷ 6，结果是8。对于 7 ÷ 0.25，两边乘以100得到 700 ÷ 25 = 28。当答案不能整除时，你可能需要按指定的小数位或有效数字给出结果。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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