Trailing zeros

To add or subtract decimal numbers, line up the decimal points and add or subtract as usual. The decimal point will be in the same place as it is in the terms. If the numbers are written across the page, set up the problem one number below the other, lining up the decimal points. You can add trailing zeros as placeholders. 

Note that in both of these last two examples, either leading zeroes or trailing zeroes were added as placeholders. 

To add a decimal and a whole number, write the problem vertically (be sure to line up the decimal points), put a decimal on the end of the whole number, and place trailing zeros next to it ... 

Write the fraction as a decimal so that it can be compared to 0.732. Because the decimal 0.732 has a digit in the thousandths place, we must round yy to the nearest ten thousandth 8 -h 11 = 0.72727272.. ., or 0.7273 to the nearest ten thousandth. Add a trailing zero to 0.732, line up the decimal points, and compare corresponding digits of the two numbers from left to right ... 

What if we rounded 7.28 to the nearest ones place We d look at the digit in the tenths place, because that is the place to the immediate right of the ones place. There is a 2 in the tenths place, so we must round down. The digit in the ones place, 7, stays the same and all digits to the right become zero. 7.28 rounded to the nearest one is 7.00. Because those zeros are trailing zeros, we can say that 7.28 rounded to the nearest one is 7. 

To make the comparison easier, add a leading zero to 5.607 and two trailing zeros to 44.1 ... 

First, line up the decimal points and add a trailing zero to the second number ... 

Start by lining up the decimal points of the three numbers and adding trailing zeros as needed ... 

Add a trailing zero to the first number and a leading zero to the second number. The first number has a 1 in the tens place and the second number has a 0 in the tens place, so the first number is bigger 16.5 is greater than 9.55. 

First, write the addition problem vertically, and put a decimal point on the end of any whole numbers. Then, place trailing zeros next to that decimal point until the whole number has the same number of digits as the decimal number ... 

Adding decimals to decimals is just like adding decimals to whole numbers. It is just as important to line up your columns and add trailing zeros as needed. 

The first addend has six digits three to the left of the decimal point and three to the right. The second addend has only two digits, one to the left of the decimal point and one to the right. Keep your columns straight and place two trailing zeros on the end of 2.3 ... 

When we added decimals to whole numbers, we placed trailing zeros at the end of the whole numbers to help us keep our columns straight. When we subtract decimals from whole numbers, we have to add trailing zeros to the end of the whole numbers. We will also have to borrow, likely more than once. 

As with addition, we begin by lining up our columns. Place two trailing zeros on the end of the minuend (44) ... 

In order to do subtraction in the hundredths place, we must borrow from the tenths place. Because the tenths place also has a 0 in it, we must borrow from the ones place. Whenever we are subtracting a decimal from a whole number, we will have to borrow from at least the ones place, and rename every trailing zero we placed at the end of the whole number. 

Line up the decimal points and place five trailing zeros on the end of 10. Then, subtract ... 

Line up the columns, place a decimal point after the subtrahend (2) and tack on five trailing zeros ... 

Line up the decimal points. Because the minuend and the subtrahend have the same number of decimal places, no trailing zeros are needed ... 

Line up the decimal points. Place a trailing zero on 74.87, subtract, and carry down the decimal point ... 

AS WITH ADDITION and subtraction, if the last digit of your answer, to the right of the decimal point is zero, then that trailing zero can be removed from your answer. But as with addition and subtraction, be sure to place the decimal point in the correct place before removing any trailing zeros. 

Now that we ve placed our decimal point with six digits to its right, we can remove the trailing zero. The product of 1.2534 and 24.05 is 30.14427. 

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