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Ordering Numbers by Size
What does it mean?
To order numbers means to arrange them from smallest to largest or largest to smallest.
This includes:
Positive and negative numbers
Fractions
Decimals
Whole numbers
How to order numbers:
Convert all numbers to the same form (e.g., all decimals or all fractions).
Compare their values one by one.
Write them in the required order.
Practice Problem:
Order from smallest to largest: –3, 0, 5, –1
Answer: –3, –1, 0, 5
Order the decimals: 0.5, 0.75, 0.25, 1
Answer: 0.25, 0.5, 0.75, 1
Using Inequality Symbols
What are they?
Inequality symbols help compare two values.
Example Comparisons:
4 > 2 - True
0.5 < 1 - True
–2 > –3 - True (remember: –2 is closer to 0)
Practice Problem
Write the correct symbol:
–1 __ 2
Answer: <
Ordering Different Numbers:
Ordering Negative Numbers
Important rule for negative numbers:
The number closer to zero is larger
The number further left on the number line is smaller
Example: compare –4 and –2:
–4 < –2 (because –4 is further left and further away from 0)
Practice Problem
Which is greater: –6 or –3?
Answer: -3 since it's closer to 0 and further to the right on the number line
Ordering Fractions
How to compare fractions:
Same denominator? Compare numerators.
Different denominators? Convert to common denominators OR convert to decimals
Examples:
3/5 and 4/5 → compare 3 and 4 → 4/5 is larger
1/2 and 3/4 → convert to decimals: 0.5 and 0.75 → 3/4 is larger
Practice Problem
Which is bigger: 2/3 or 3/5?
Answer: convert to decimals: 0.67 and 0.6 → 2/3 is larger
Ordering Decimals
Tip: line up decimals digit by digit (use zeros to help).
Example: order: 0.5, 0.25, 0.3
Add zeros to match digits:
0.50, 0.25, 0.30 → ordered = 0.25, 0.30, 0.50
Practice Problem
Arrange: 0.4, 0.45, 0.05 from smallest to largest
Answer: 0.40, 0.45, 0.05 → 0.05, 0.4, 0.45
NOTES DONE BY FARIDA SABET
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