Working with Decimals

I. Place Value

A few of the place value names when working in base 10 are as follows:

a b c d . e f g

On the left side of the decimal point:

a: thousands place b: hundreds place c: tens place
d: ones place

On the right side of the decimal point:

e: tenths place f: hundredths place g: thousandths place

We can write any number using these place values. This is called the expanded form of the number:
2,614.537= 2·1000 + 6·100 + 1·10 + 4·1 + + +

Example

Write .57 as a fraction.

Solution

II. Rounding

Often, we need to approximate decimal numbers by rounding. The usual method of rounding is demonstrated in the following examples.

Example 1

Round 123.456789 to the nearest hundredth.

Solution 1

Since the digit in the thousandths place (the next place to the right of the hundredths place) is a 6 and 6 is greater than or equal to 5, round the hundredths digit up.

The rounded value is 123.46.

Example 2

Round 789.456123 to the nearest thousandth.

Solution 2

Since the digit in the ten thousandths place is 1 and 1 is less than 5, keep the thousandth digit the same.

The rounded value is 789.456.

Example 3

Round 358.45 to the nearest whole number.

Solution 3

The digit in the tenths place is a 4 and 4 is less than 5.

The rounded value is 358.