Decimals show parts of a whole by using place value to the right of the decimal point. The first place after the decimal point is tenths, and the second place is hundredths. This helps us describe amounts that are between whole numbers, such as money, measurements, and points on a number line.
Understanding tenths and hundredths makes it easier to compare, add, and subtract decimal numbers.
Understanding Decimals
Place value works because each step to the right splits the unit into ten equal pieces. A whole can be cut into ten tenths. Each tenth can be cut into ten smaller equal pieces, making one hundred equal pieces altogether.
This repeating pattern continues to thousandths and beyond. The digits do not become less important because they are farther right. Their values become smaller.
A digit in the hundredths place is worth one tenth as much as the same digit in the tenths place. This idea explains why moving a decimal point changes a number so strongly when multiplying or dividing by ten, one hundred, or one thousand.
Decimals connect closely with fractions. A decimal with one digit after the point can be read as a fraction with ten as the denominator. A decimal with two digits can be read as a fraction with one hundred as the denominator.
For example, zero point twenty five means twenty five parts out of one hundred equal parts. It can be simplified to one quarter.
Seeing these connections helps when changing between fractions, decimals, and percentages. A percentage is based on one hundred, so zero point twenty five, twenty five hundredths, one quarter, and twenty five percent describe the same amount.
Zeros at the end of a decimal deserve careful attention. Adding zeros to the right does not change the value. For example, three point five and three point five zero name the same point on a number line.
The extra zero can still be useful because it keeps place values lined up during calculations. When adding or subtracting, write numbers in columns with their decimal points directly under each other. Then add or subtract within matching places.
Tenths belong with tenths, and hundredths belong with hundredths. A common error is lining up the last digits instead. That can mix values of different sizes and give an incorrect answer.
Decimals appear whenever a whole unit is divided into smaller units. Money uses hundredths of a dollar. A price of two dollars and seven cents is written as two point zero seven dollars, not two point seven dollars.
Lengths on rulers can use tenths of a centimetre. Masses, temperatures, sports times, and digital measurements often use decimals too. Estimation is a useful check in every setting.
Before calculating, decide which nearby whole number a decimal is close to. A result near ten may be reasonable when adding four point eight and five point three. A result near one would show that something went wrong.
Students should practice reading each decimal aloud by place value, drawing it on grids, and locating it between whole numbers. These methods build meaning beyond memorising rules.
Key Facts
- In 1.34, the 1 means 1 one, the 3 means 3 tenths, and the 4 means 4 hundredths.
- 1 tenth = 0.1 = 1/10.
- 1 hundredth = 0.01 = 1/100.
- 10 hundredths = 1 tenth, so 0.10 = 0.1.
- 1.34 = 1 + 0.3 + 0.04 = 1 + 3/10 + 4/100.
- To compare decimals, line up the decimal points and compare digits from left to right.
Vocabulary
- Decimal
- A decimal is a number that uses a decimal point to show whole number parts and fractional parts.
- Tenths
- Tenths are one of ten equal parts of a whole and are written in the first place to the right of the decimal point.
- Hundredths
- Hundredths are one of one hundred equal parts of a whole and are written in the second place to the right of the decimal point.
- Place value
- Place value is the value of a digit based on its position in a number.
- Decimal point
- The decimal point separates the whole number part from the fractional part of a decimal.
Common Mistakes to Avoid
- Reading 1.34 as one point thirty-four without understanding place value. The 3 means 3 tenths and the 4 means 4 hundredths, not 34 whole units.
- Thinking 0.4 is smaller than 0.34 because 4 has fewer digits. This is wrong because 0.4 = 0.40, and 40 hundredths is greater than 34 hundredths.
- Forgetting to line up decimal points when adding or subtracting. Digits must be placed in matching place-value columns, such as ones under ones and tenths under tenths.
- Believing that adding a zero at the end changes the value of a decimal. A zero at the end after the decimal does not change the value, so 0.5 = 0.50.
Practice Questions
- 1 Write 2.47 in expanded form using ones, tenths, and hundredths.
- 2 Which is greater, 0.6 or 0.58? Explain using hundredths.
- 3 A model shows one whole square shaded, three tenths shaded, and four hundredths shaded. Explain why the decimal is 1.34.