Adding, Subtracting, Multiplying, and Dividing Decimal Numbers

Warm-Up List the first 10 multiples of 8. 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 Count by 8s from 2 to 50. 2, 10, 18, 26, 34, 42, 50 Simplify the fraction: 6/9 2/3 Simply the fraction: 12/9 1 1/3 Simply the fraction: 24/9 2 2/3

Place Value A whole number consisting of only one digit only has a number in the ones place. For example, 8 is a whole number consisting of only one digit; the 8 is in the ones place. A whole number consisting of two digits will have a number in the tens place and a number in the ones place. For example, 18 is a whole number consisting of two digits; the 1 is in the tens place and the 8 is in the ones place.

Decimal Places When a decimal number has only one digit after the decimal, that number is in the tenths place. When a decimal number has two digits following the decimal, the numbers are in the tenths place and the hundredths place. Three digits after the decimal would fill the tenths, hundredths, and thousandths places.

Aligning the Decimal, Place Value When adding or subtracting fractions, we align the decimal point because that will align the digits of the same place value. If we have a whole number without a decimal, we write in a decimal after the ones place. We can fill any decimal place with zero so that each number has the same place values filled with digits.

Example

Example

Review Which digit in 4.65 has the same place value as the 2 in 12? 4, both the 4 and the 2 are in the ones place Which digit in 13.65 has the same place value as the 8 in 7.834? 6, both the 6 and the 8 are in the tenths place Which digit in 100.401 has the same place value as the 9 in 834.229? 1, both the 9 and the 1 are in the thousandths place

Practice

Simplifying Numbers We communicate numbers in their simplest forms. One way to simplify numbers is to remove unnecessary zeroes. We can remove zeroes from the front of whole numbers. 0023 can be simplified by removing the zeroes in front of the tens and ones places, leaving 23.

Simplifying Decimal Numbers We can also remove zeroes at the end of decimal numbers. 23.400 can be simplified by removing the two zeroes in the hundredths and thousandths places, leaving 23.4. 09.200 can be simplified by removing the zero in the ones place, hundredths place, and thousandths place, leaving 9.2.

Practice

Subtracting Decimal Numbers For some subtraction problems, we need to add decimal places to perform the subtraction. If we subtract 0.23 from 0.4, we first fill the hundredths place with a zero then we subtract.

Example

Example

Practice

Reading Decimal Numbers Use words to name 12.625. twelve and six hundred twenty-five thousandths

Comparing Decimal Numbers When we compare the highest decimal place value, we see that 5 (in the tenths place) is greater than 4 (also in the tenths place).

Ordering Decimal Numbers

Practice

Multiplying Decimal Numbers

Multiplying Decimal Numbers

Multiplying Decimal Numbers

Multiplying Decimal Numbers When we set up a decimal multiplication problem, we do not line up the decimal points as we do in addition and subtraction. We just set up the problem as though it were a whole-number problem and then multiply. To place the decimal point in the answer, we first count the total number of decimal places in both factors. Then we insert a decimal point in the answer so that is has the same total number of decimal places as the factors.

Examples

Practice

Zeroes as Placeholders Sometimes there are more decimal places in the factors than there are digits in the product. To complete the multiplication, we fill the empty place(s) with a zero(es).

Zeroes as Placeholders

Example

Practice