Decimal Place Value Relationships
Decimal place value relationships is a Grade 5 math skill in enVision Mathematics, Chapter 1: Understand Place Value. Students learn that each decimal digit is 10 times the value of the digit to its right and 1/10 the value of the digit to its left, applying the same base-ten structure to tenths, hundredths, and thousandths as exists for whole number places.
Key Concepts
Property The value of a digit in a decimal number is $10$ times the value of the digit to its right and $\frac{1}{10}$ the value of the digit to its left.
Examples In the number $0.22$, the value of the $2$ in the tenths place ($0.2$) is 10 times the value of the $2$ in the hundredths place ($0.02$). In the number $0.888$, the value of the $8$ in the hundredths place ($0.08$) is $\frac{1}{10}$ the value of the $8$ in the tenths place ($0.8$). In $0.055$, the value of the $5$ in the hundredths place ($0.05$) is 10 times the value of the $5$ in the thousandths place ($0.005$).
Explanation Our number system is based on powers of ten. As you move from left to right on the place value chart, the value of each position is one tenth of the value of the position to its left. This means a digit in one place is ten times as great as the same digit in the place to its right. This relationship holds true for both whole numbers and decimals.
Common Questions
What is the relationship between adjacent decimal places?
Each place is 10 times the value of the place to its right and 1/10 the value of the place to its left. For example, tenths is 10 times hundredths.
How much is 1 tenth compared to 1 hundredth?
1 tenth equals 10 hundredths. The tenths place is 10 times larger than the hundredths place.
How does decimal place value extend whole number place value?
The same pattern continues past the ones place: tenths, hundredths, thousandths, and so on, each worth 1/10 of the place before it.
Where are decimal place value relationships taught in enVision Grade 5?
Chapter 1: Understand Place Value in enVision Mathematics, Grade 5.
Why does understanding decimal place value matter?
It is the foundation for comparing, ordering, adding, subtracting, multiplying, and dividing decimals accurately.