Understanding decimals.

Source*: Online Learning Center


A decimal is a kind of fraction. It expresses a part of a whole.

The decimal point separates whole numbers from decimal places.

All decimal place names end in -ths.

To read a whole number and decimal, follow these steps:

Say the whole number first.

Say the word and for the decimal point.

Read the decimal as though it were a whole number.

Give the decimal a name according to the number of places it holds (tenths, hundredths, thousandths, and so on).

QUIZ: The digit 6 in the number 0.936 is equal to which of the following?

A) six tenths
B) six hundredths
C) six thousandths
D) six ten-thousandths
E) six hundred-thousandths

To write a decimal, follow these steps:

Think about the number of decimal places you need.

Use zeros to hold places where necessary.

Remember the word and separates whole numbers from decimal fractions.

Rounding is a useful tool for estimating answers to decimal problems.

QUIZ: Write three thousand forty-eight ten-thousandths in decimal form.

A) 0.03048
B) 0.3048
C) 0.348
D) 3000.48
E) 0.0348


To round a decimal, follow these steps:

Underline the digit in the place to which you are rounding.

 If the digit to the right of the underlined digit is greater than or equal to 5, add 1 to the underlined digit.

If the digit to the right of the underlined digit is less than 5, leave the underlined digit as it is. Drop the digits to the right of the underlined digit.

Adding and Subtracting Decimals 

To add decimals, follow these steps:

1.  Line up the decimals, with decimal point under decimal point.
2. Add each column.
3. Place the decimal point in the answer directly below the decimal points
4. above.

To subtract decimals, follow these steps:

1. Line up the decimals, with decimal point under decimal point. 
2. Subtract. 
3. Place the decimal point in the answer directly below the decimal points

Quiz: From a board that was 2 meters long, Matt cut a piece that was 1.65 meters long. Assuming no waste, how long was the remaining piece?

A) 3.65 m

B) 2.35 m

C) 1.35 m

D) 0.65 m

E) 0.35 m

Multiplying and Dividing Decimals

To multiply decimals, follow these steps:

1. Put the number with more digits on top and the other below.
2. Multiply as you would multiply whole numbers.
3. Count the number of decimal places in both of the numbers you multiplied.
4. Put the total number of decimal places in the answer.

QUIZ: Find the product of 5.09 and 1.4 rounded to the nearest tenth.

A) 7.126

B) 7.13

C) 7.1

D) 7

E) 10

To divide decimals, follow these steps:

1. Make the divisor a whole number by moving the decimal point to the right.
2. Move the decimal point in the dividend the same number of places.
3. Divide as you would with whole numbers.
4. Place the decimal point in the answer directly above its new position in the dividend.

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