Comparing Decimal Numbers
Comparing decimal numbers is simplified in Grade 6 Saxon Math Course 1 by attaching trailing zeros so both numbers have the same number of decimal places. Since trailing zeros do not change a decimal's value (0.7 = 0.70 = 0.700), the comparison becomes a straightforward digit-by-digit comparison from left to right. To order 0.8, 0.75, 0.801, 0.08 from least to greatest, rewrite as 0.800, 0.750, 0.801, 0.080 and compare: 0.080 < 0.750 < 0.800 < 0.801.
Key Concepts
Property To compare decimal numbers, it is helpful to attach trailing zeros so that both numbers have the same number of decimal places. Zeros at the end of a decimal number do not change its value: $0.3 = 0.30 = 0.300$.
Examples Compare $0.4$ and $0.404$: $0.400 < 0.404$, so $0.4 < 0.404$. Compare $0.8$ and $0.79$: $0.80 0.79$, so $0.8 0.79$. Compare $2.5$ and $2.50$: $2.50 = 2.50$, so $2.5 = 2.50$.
Explanation Comparing decimals can be tricky! Is $0.5$ bigger than $0.499$? To make it a fair fight, add trailing zeros to give them the same number of decimal places. Think of it like comparing '500 thousandths' to '499 thousandths'—much easier, right? This trick helps you see which number truly holds the greater value without getting confused!
Common Questions
Is 0.7 greater than 0.69?
Yes. Rewrite as 0.70 vs 0.69. Compare tenths: 7 > 6, so 0.70 > 0.69.
Order 0.8, 0.75, 0.801, 0.08 from least to greatest.
Rewrite: 0.800, 0.750, 0.801, 0.080. Order: 0.080 < 0.750 < 0.800 < 0.801.
Does adding trailing zeros change a decimal's value?
No. 0.5 = 0.50 = 0.500. Trailing zeros after the last nonzero decimal digit do not change the value.
What is the first step when comparing two decimals?
Make both decimals the same length by adding trailing zeros, then compare digit by digit from the leftmost decimal place.
How do you compare 0.4 and 0.400?
They are equal: 0.4 = 0.400.