Write & Compare Decimals
How do we read, write, and compare decimal numbers?
š Standards & Objectives
- Write decimals in standard, expanded, and word form
- Compare two decimals using <, >, and = symbols
- Order a set of decimals from least to greatest or greatest to least
š Decimals Are Everywhere!
$3.459
Why not just write $3.46?
9.58 seconds
Usain Bolt's 100m world record
.342
Is .342 better or worse than .339?
Today we'll learn how to read, write, and compare decimals ā skills you'll use every day!
š Key Vocabulary
Standard Form
Click to reveal!
A number written with digits only
Example: 4,518.765
Expanded Form
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Shows the value of each digit
Example: 4,000 + 500 + 10 + 8 + 0.7 + 0.06 + 0.005
Word Form
Click to reveal!
Written using words
Example: four thousand, five hundred eighteen and seven hundred sixty-five thousandths
Compare
Click to reveal!
Decide which is greater, lesser, or equal
Use symbols: < > =
āØ Three Forms of Decimals
Every decimal number can be written in three ways. Let's look at the number 93,726.485:
š Standard Form
93,726.485
š Expanded Form
90,000 + 3,000 + 700 + 20 + 6 + 0.4 + 0.08 + 0.005
š Word Form
ninety-three thousand, seven hundred twenty-six and four hundred eighty-five thousandths
š Converting Between Forms
Standard ā Expanded
Write the value of each digit separately, then connect with + signs
Standard ā Word
Read the whole number part, say "and" at the decimal point, then read the decimal digits followed by the last place value name
Word ā Standard
Write the whole number, add a decimal point where it says "and," then write the decimal digits
Key Tip: The word "and" = the decimal point. "Four hundred eighty-five thousandths" means .485 (three decimal places because thousandths = 3 places)
šļø Problem 1
šļø Problem 2
š„ Problem 3
š„ Problem 4
āļø Problem 5
āļø Problem 6
āØ Comparing Decimals
When comparing decimals, we look at one place value at a time, starting from the left. The first place where the digits differ tells us which number is greater!
Write numbers vertically, lining up the decimal points:
4.976
Ones are the same (4 = 4). Tenths differ: 2 < 9
4.278 < 4.976
Since 2 tenths < 9 tenths, we know 4.278 is less than 4.976. We don't even need to check hundredths or thousandths!
š How to Compare Decimals
Line up the decimal points
Write the numbers one above the other so that matching place values are aligned
Add trailing zeros if needed
Make sure both numbers have the same number of decimal places (e.g., 3.5 becomes 3.500)
Compare from left to right
Start at the greatest place value. The first place where digits differ tells you the answer!
Write the comparison symbol
Use < (less than), > (greater than), or = (equal to)
Remember: The "alligator" always eats the bigger number! š The open mouth points toward the greater value.
šļø Problem 7
šļø Problem 8
š„ Problem 9
š„ Problem 10
āļø Problem 11
āļø Problem 12
āØ Ordering Decimals
Ordering decimals means putting a group of numbers in order from least to greatest or greatest to least. We use the same compare-by-place strategy ā just with more numbers!
Start with the smallest number and work up.
Start with the biggest number and work down.
Pro Tip: Compare two numbers at a time. Find the smallest (or largest), write it first, then repeat with the remaining numbers!
š How to Order Decimals
Line up decimal points & add trailing zeros
Write all numbers vertically with the same number of decimal places
Compare pairs from left to right
Use the comparing strategy to figure out which is smallest and which is greatest
Write the final order
Arrange the numbers from least to greatest or greatest to least as requested
Watch Out: Different numbers of whole-number digits? Check those first! 63.602 is way less than 639.26 because 63 < 639 in the whole-number part.
šļø Problem 13
šļø Problem 14
š„ Problem 15
āļø Problem 16
š„ Problem 17 ā Challenge!
5,000 + 200 + 0.08 + 0.003
Ben says his number in word form is:
"five thousand, two hundred and eighty-four thousandths"
Who has the greater number?
š Problem 18 ā Word Problem
Marcus: 12.09 seconds Jade: 12.9 seconds Kai: 12.019 seconds
Order the runners from fastest (least time) to slowest (most time).
š¬ Turn & Talk
Your friend says: "12.5 is less than 12.489 because 12.489 has more digits after the decimal."
Is your friend correct? How would you explain their mistake? Use place value vocabulary in your answer.
The friend is wrong! Number of digits doesn't determine value. Add a trailing zero: 12.500 vs 12.489. Now compare tenths: 5 > 4, so 12.5 > 12.489. The tenths place already tells us which is greater ā more digits does NOT mean a bigger number!
š Key Takeaways
Three Forms
Standard: 4,518.765
Expanded: 4,000 + 500 + 10 + 8 + 0.7 + 0.06 + 0.005
Word: four thousand, five hundred eighteen and seven hundred sixty-five thousandths
Comparing
Line up decimal points. Add trailing zeros. Compare left to right. First different digit decides the answer!
Ordering
Compare pairs. Find the smallest (or largest). Write it first, then repeat! More digits ā bigger number.
#1 Tip: Always add trailing zeros so every number has the same number of decimal places before comparing!
š« Exit Ticket
Complete these three problems on your exit ticket paper. Show your work!
6,803.29
6,000 + 800 + 3 + 0.2 + 0.09
9.072 < 9.27 (0 tenths < 2 tenths)
4.56 4.506 4.6
4.506 < 4.56 < 4.6