Representing Tenths and Hundredths as Decimals
Representing Tenths and Hundredths as Decimals is a Grade 4 math skill from Pengi Math that teaches students the positional notation for decimal fractions — that 0.1 means one tenth and 0.01 means one hundredth. The decimal point separates the whole number part from the fractional part, with each position to the right representing a place value ten times smaller than the position to its left. This foundational 4th grade concept is the gateway to understanding all decimal numbers and operations.
Key Concepts
Property A tenth is one part of a whole that is divided into 10 equal parts. A hundredth is one part of a whole divided into 100 equal parts. We can write them as decimals: $$ \text{one tenth} = 0.1 $$ $$ \text{one hundredth} = 0.01 $$.
Examples A whole is divided into 10 equal parts. If 3 parts are shaded, the decimal is 0.3 . A whole is divided into 10 equal parts. If 7 parts are shaded, the decimal is 0.7 . A whole is divided into 100 equal parts. If 45 parts are shaded, the decimal is 0.45 . A whole is divided into 100 equal parts. If 12 parts are shaded, the decimal is 0.12 .
Explanation Tenths and hundredths represent parts of a whole using decimal notation. The position of a digit to the right of the decimal point shows how the whole is divided — into 10 equal parts for tenths and 100 equal parts for hundredths. The digits in these places describe how many parts of the whole are being represented, allowing us to express and understand amounts that are less than one whole.
Common Questions
What does the decimal point mean in a number?
The decimal point separates the whole number part (to its left) from the fractional part (to its right). Digits to the right of the decimal point represent fractions: the first digit after the decimal is tenths, the second is hundredths, the third is thousandths, and so on.
What does 0.1 mean?
0.1 means one tenth — one part out of 10 equal parts of a whole. If you divide a dollar into 10 equal pieces, each piece is 0.1 dollars (10 cents). 0.1 is the decimal form of the fraction 1/10.
What does 0.01 mean?
0.01 means one hundredth — one part out of 100 equal parts of a whole. 0.01 is the decimal form of the fraction 1/100. One cent ($0.01) is exactly one hundredth of a dollar, which is why money is a great model for hundredths.
How many hundredths are in one tenth?
There are 10 hundredths in one tenth. Since 0.1 = 0.10 = 10/100, one tenth equals ten hundredths. Each place value in the decimal system is ten times the value of the place to its right.
When do 4th graders learn to represent tenths and hundredths?
Tenths and hundredths as decimals are introduced in 4th grade math. Pengi Math Grade 4 teaches this as the foundation of the decimal system, connecting fraction notation (1/10) to decimal notation (0.1).
How is the tenths place different from the tens place?
The tens place is to the LEFT of the ones place (e.g., the 2 in 25 represents 20). The tenths place is to the RIGHT of the decimal point (e.g., the 2 in 0.2 represents 2/10). 'Tens' is a whole number place; 'tenths' is a fractional place.
Which textbook covers tenths and hundredths as decimals for 4th grade?
Pengi Math Grade 4 introduces representing tenths and hundredths as decimals in the place value unit, establishing the decimal notation system as the foundation for all decimal work.