# Rounding Off Decimals

## Objectives

After completing this unit, you should be able to:

• Determine whether a decimal should be rounded up or down.
• Round up decimals.
• Round down decimals.

## Rounding Off

Rounding off a decimal is a technique used to estimate or approximate values. Rounding is most commonly used to limit the amount of decimal places. Instead of having a long string of decimals places, or even one that goes on forever, we can approximate the value of the decimal to a specified decimal place.

We can round to any place. After rounding, the digit in the place we are rounding will either stay the same, referred to as rounding down, or increase by 1, referred to as rounding up. The question now becomes, when do we round up or down?

### When to Round Up

Rounding up means that we increase the terminating digit by a value of 1 and drop off the digits to the right. If the next place beyond where we are terminating the decimal is greater than or equal to five, we round up. For example, if we round 5.47 to the tenths place, it can be can be rounded up to 5.5.

### When to Round Down

If the number to the right of our terminating decimal place is four or less (4, 3, 2, 1, 0), we round down. This is done by leaving our last decimal place as it is given and discarding all digits to its right. For example, if we round 6.734 to the hundredths place, it can be rounded down to 6.73.

### Example

Round 0.24 to the tenths place.

 We wish to round 0.24 to the tenths place. That means we only want one digit to appear after the decimal point, so .24 will round to .2 or .3, whichever is closer. There is a 4 in the hundredths place. Since this is less than 5, we round down, meaning we leave the 2 in the tenths place and drop the 4 off the end.

### Example

Round 12.756 to the tenths place.
The number 12.756 should be rounded up to 12.8.

 We wish to round 12.756 to the tenths place. That means we only want one digit to appear after the decimal point. In this example, there are two digits that appear to the right of the tenths place. When rounding off 12.756, look only at the digit in the place directly to the right of the tenths place (the hundredths place). Check to see if the digit in the hundredths place is 5 or greater or less than 5. In this case the digit in the hundredths place is a 5, therefore we round up from 7 to 8.

## Rounding Off in Everyday Life

Rounding occurs all the time in everyday life. For example, cash registers are programmed to round off automatically to the nearest hundredth. Since one cent is one hundredth of a dollar, what we are charged must be rounded off to the hundredths place. For example, if the sales tax is 8.25%, or .0825, you could have the following table of taxes charged for different sale amounts.

Amount of Sale (dollars) Sales Tax* (dollars) Total Amount (dollars)
5.00 .41 5.41
10.50 .87 11.37
20.75 1.71 22.46
31.00 2.56 33.56
55.50 4.58 60.08
78.75 6.50 85.25
*Sales tax is charged at the rate of 8.25%

The middle column, Sales Tax, was obtained by multiplying the first column by 0.0825, which is the rate of sales tax.

Amount of Sale x 0.0825 = Sales Tax

Notice that the Sales Tax column only goes out to the hundredths place. Let's try this multiplication for a couple of rows to determine if the creators of the table used rounding without telling us.

### First Row

Amount of Sale = \$5.00
Sales Tax Rate = 0.0825

5.00 x .0825 = 0.4125

On the table, the Sales Tax is listed as 0.41. As we can see, the Sales Tax was rounded down to the closest cent.

### Second Row

Amount of Sale = \$10.50
Sales Tax Rate = 0.0825

10.50 x .0825 = .86625

On the table, the Sales Tax is listed as 0.87. Here we can see, the Sales Tax was rounded up to the closest cent.

This table gives a typical example of how rounding is used everyday.

Now that you've had a chance to read about rounding off decimals, and seen a real life example, try the practice on rounding off the decimals.