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# Decimals

## Rounding Decimals

Rounding is frequently used to give an estimate of a given number. For example, the balance of a savings account shows the amount to the nearest cents. But when the number is big, such as in a govenment's budget, we may estimate the amount by rounding it to the nearest millions or even billions of dollars.

Let us call the digit at the place value you are interested in the rounding digit.

(I) Rounding a whole number:

If the rounding digit is at the ones position, then there is nothing to do. Otherwise, look at the digit just to rthe right of it.

1. If that digit is less than 5, do not change the rounding digit but change all the digits to the right of the rounding digit to zero.

2. If that digit is greater than or equal to 5, add one to the rounding digit and change all digits to the right of the rounding digit to zero.

### Example 1

Round the given number to the place value indicated.

 rounded to the nearest is

### Exercise 1

Round the given number to the place value indicated.

 rounded to the nearest is

(II) Rounding a decimal number:

If the rounding digit lies to the left of a decimal point, then drop all digits after the decimal point and proceed as in (I). Otherwise, look at the digit just to the right of the rounding digit.

1. If that digit is less than 5, do not change the rounding digit and drop all digits to the right of the rounding digit.

2. If that digit is greater than or equal to 5, add one to the rounding digit and drop all digits to the right of the rounding digit.

### Example 2

Round the given number to the place value indicated.

 rounded to the nearest is

### Exercise 2

Round the given number to the place value indicated.

 rounded to the nearest is

Note: If the number represents a sum of money, then

"rounding to the nearest hundredths" = "rounding to the nearest cents",

"rounding to the nearest ones" = "rounding to the nearest dollars".

For example, \$100.486 to the nearest cents is \$100.49 and to the nearest dollars is \$100.

It is easier to say, and therefore more common to say, "round to one, two, three etc decimal places (d.p.)" than "round to the nearest 10ths, 100ths, 1000ths etc".

### Exercise 3

Round the given number to the number of decimal places indicated.

 rounded to the nearest is