What You Will Learn
- Understand what decimals represent.
- Identify decimal place values.
- Read, write, compare and order decimals.
- Add, subtract, multiply and divide decimals.
- Use decimals in everyday situations.
What Are Decimals?
Decimals are numbers that use a decimal point to show a whole number together with a part of a whole. The digits to the left of the decimal point represent whole-number places, while digits to the right represent fractional place values.
A decimal can also represent a fraction with a denominator based on powers of 10. For example, 0.5 means five tenths and is equal to 1/2.
Decimal Place Value
Place value tells us the value represented by each digit. After the decimal point, the first place is tenths, followed by hundredths, then thousandths.
In 47.528, the 5 is in the tenths place, the 2 is in the hundredths place and the 8 is in the thousandths place.
Reading and Writing Decimals
Read the whole-number part first, then read the decimal part according to its place value.
Three and four tenths.
Seven and twenty-five hundredths.
Trailing zeros do not change the value of a decimal: 0.5 = 0.50 = 0.500.
Comparing Decimals
Compare the whole-number parts first. If they are equal, compare the digits after the decimal point from left to right.
Compare 0.62 and 0.7. Write 0.7 as 0.70. Since 62 hundredths is less than 70 hundredths:
Ordering Decimals
To order decimals, compare their place values carefully. Adding zeros to the right can make the comparison easier.
Order 1.4, 1.08, 1.35, 1.5 from smallest to largest.
Therefore, 1.08 < 1.35 < 1.4 < 1.5.
Adding Decimals
Line up the decimal points before adding. This keeps matching place values in the correct columns.
Writing 3.70 rather than 3.7 helps keep the place values aligned.
Subtracting Decimals
As with addition, line up the decimal points and subtract corresponding place values.
Zeros can be added to the right of a decimal without changing its value.
Multiplying Decimals
Multiply the numbers as whole numbers first, then place the decimal point by counting the total number of decimal places in the factors.
Dividing Decimals
When dividing by a whole number, divide normally and keep the decimal point in the appropriate position. When the divisor is a decimal, the divisor can be converted to a whole number by shifting both decimal points equally.
Three groups of 2.4 make 7.2.
Decimals in Everyday Life
Decimals are commonly used for money, measurements, distances, weights, temperatures and other quantities.
Amounts of money are often written using two decimal places.
Decimals allow measurements to be expressed more precisely.
Common Mistakes
Remember that 0.8 is greater than 0.75 because 0.80 is greater than 0.75.
Line up decimal points before adding or subtracting.
0.6, 0.60 and 0.600 have the same value.
Quick Practice
Try these questions before checking the answers.
What is the value of the 7 in 4.72?
Which is greater: 0.6 or 0.56?
Calculate: 12.5 + 3.75.
Calculate: 9.4 − 2.65.
Calculate: 2.5 × 4.
Summary
- Decimals represent whole numbers and parts of a whole.
- The decimal point separates whole-number places from decimal places.
- Tenths, hundredths and thousandths are common decimal place values.
- Decimal points should be aligned when adding or subtracting.
- Zeros at the end of a decimal do not change its value.