Rounding Decimals
Decimal Numbers
A number that contains a decimal point is called a “decimal number” or a “decimal.” Decimals are
a part of the Base-10 number system just like whole numbers. Decimals are also based on a
simple pattern of tens, where each place is ten times the value of the place to its right. This
pattern is known as a ten-to-one place-value relationship.
Let’s place decimal numbers on a place value chart through the thousandth place.
(100)
(10)
(1)
hundreds
tens
ones
10 x 10
10 x 1
10 x 0.1
.
(0.1)
(0.01)
(0.001)
tenths
hundredths
thousandths
10 x 0.01
10 x 0.001
10 x 0.0001
Decimal point
Remember that a decimal point separates the whole number places from the places that are
less than one. Place values extend or continue infinitely in two directions from a decimal point.
When we read decimals, we read them in a specific way:
1. First, read the whole number to the left of the decimal point;
2. Next, read the decimal point as “and;”
3. Then, read the digits to the right of the decimal point like we would read a whole
number;
4. Finally, locate the digit in the smallest place and say the name of its place value.
Also, like whole numbers, there are 3 different forms for writing decimals. There is a standard
form, a written form, and the expanded form.

Standard form: 23.456

Written:
twenty-three and four hundred fifty-six thousandths

Expanded:
(2 x 10) + (3 x 1) + (4 x 0.1) + (5 x 0.01) + (6 x 0.001)
PRACTICE!
1. Write the decimal 8.486 using a place value chart.
2. Read 8.486 to a classmate.
3. Write 8.486 using standard, written, and expanded form.
Rounding Decimal Numbers
Rounding Decimals
Decimal numbers can be very long, and we may need to round them for everyday use.
As consumers, we often round the cents to dollars to make it easy to determine if we have
enough money for a purchase. For instance, if the price of a DVD is $17.97, we round it to $18.
The way we round decimals is similar to the way we round whole numbers:
1. Look one place to the right of the digit we want to round to.
2. If the digit to the right is 5 or greater, add 1 to the digit in the rounding
place and change the digits to the right of the rounding place to zero.
3.
If the digit to the right is less than 5, leave the digit in the rounding
place as it is and change the digits to the right of the rounding place to
zero.
4. When we write the new number, we can drop the end zeros.
Here are some examples:
Round 15.436 to the nearest hundredth:
15.436
15.440
15.44
1. The digit to the right is 6.
2. Since 6 > 5, add 1 to 3.
3. Change the 6 to zero.
4. The zero can then be dropped.
Let’s round the same number in the example above, 15.436, to the nearest tenth:
1. The digit to the right is 3.
15.436
2. Since 3< 5, leave 4 in the tenths place.
15.400
3. Change all the numbers to the right to zeros.
15.4
4. The zeros can be dropped.
Another strategy for rounding decimal numbers is using a number line. When we use a
number line, we can see whether a number is closer to one number or another.
Rounding Decimals
Even with a number line, we have to remember that 5 is the half-way mark for determining
whether we round up or leave the digit we are rounding to as it is.
Let’s use a number line to round 18.83 to the nearest tenth.
18.83
18.8
18.85
18.9
18.85 is half-way between 18.8 and 18.9
18.83 < half-way (18.85)
18.83 is closer to 18.8 than to 18.9, so we round down to 18.8
PRACTICE!
1. Round 1.648 to the nearest hundredths.
2. What is the place value of the 7 in 425.837?
3. Round 30.503 to the nearest whole number.
4. Estimate the following sum: 0.467 + 0.248
Be prepared to defend your answer.