Mathematics
Grade 5
15 min
Place values in decimal numbers
Place values in decimal numbers
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1
Introduction & Learning Objectives
Learning Objectives
Identify the place value of each digit in a decimal number up to the thousandths place.
Read and write decimal numbers correctly from word form and standard form.
Represent decimal numbers using place value charts.
Express decimal numbers in expanded form, showing the value of each digit.
Compare and order decimal numbers based on their place values.
Explain the relationship between decimal place values and fractions with denominators of 10, 100, and 1000.
Ever wondered how stores price items like a candy bar for $1.25 or a drink for $2.79? 💰 It all comes down to understanding decimal numbers!
In this lesson, you'll discover the secret behind decimal numbers: place value! We'll explore how the position of each digit, especially after the decim...
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Key Concepts & Vocabulary
TermDefinitionExample
Decimal NumberA number that includes a whole number part and a fractional part, separated by a decimal point.3.14, 0.5, 12.007 are all decimal numbers.
Decimal PointThe dot that separates the whole number part from the fractional part in a decimal number.In 5.67, the dot between the 5 and the 6 is the decimal point.
Place ValueThe value of a digit based on its position in a number. For decimals, positions to the right of the decimal point represent parts of a whole.In 0.25, the '2' is in the tenths place, and the '5' is in the hundredths place.
Tenths PlaceThe first digit to the right of the decimal point, representing parts of ten (1/10).In 0.7, the '7' is in the tenths place, meaning 7/10 or seven tenths.
Hundredths PlaceThe second dig...
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Core Formulas
Decimal Place Value Pattern
$... \text{Hundreds}, \text{Tens}, \text{Ones} . \text{Tenths}, \text{Hundredths}, \text{Thousandths} ...$
This rule illustrates the pattern of place values. As you move one place to the right from the decimal point, the value of the place becomes one-tenth of the previous place. The decimal point separates the whole number part from the fractional part.
Value of a Digit in a Decimal
$\text{Value of Digit} = \text{Digit} \times \text{Place Value}$
To find the actual value contributed by any digit in a decimal number, multiply the digit itself by the value of its position. For example, in 0.3, the value of 3 is $3 \times \frac{1}{10} = 0.3$.
Decimal to Fraction Equivalence
$0.d_1 = \frac{d_1}{10}$, $0.d_1d_2 = \frac{d_1d_2}{100}$, $0.d_1d_2d_...
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Challenging
A student was asked to write 'fifty and five hundredths' in standard form. They wrote 50.5. What was the student's error?
A.They confused the hundredths place with the tenths place.
B.They put the decimal point in the wrong place.
C.They confused the whole numbers fifty and five.
D.They wrote the whole number part incorrectly.
Challenging
I am a decimal number between 0.3 and 0.5. The digit in my hundredths place is double the digit in my tenths place. The sum of my tenths and hundredths digits is 12. What number am I?
A.0.36
B.0.39
C.0.48
D.0.57
Challenging
A number is written in expanded form as (8 x 10) + (3 x 1/100) + (5 x 1/1000). What is this number in standard form?
A.8.35
B.80.305
C.80.0305
D.80.035
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