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Order multiple decimal numbers from least to greatest or greatest to least. Get step-by-step solutions showing how to compare decimals by place value.
Ordering decimals involves comparing the place values of each digit from left to right:
Write numbers vertically with decimal points lined up.
Start from the leftmost digit and work right.
Pad shorter decimals with zeros for easier comparison.
| Hundreds | Tens | Ones | . | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|---|
| 100 | 10 | 1 | . | 0.1 | 0.01 | 0.001 |
| 2 | 4 | 5 | . | 6 | 7 | 8 |
| This represents: 245.678 (two hundred forty-five point six seven eight) | ||||||
0.5 is actually greater than 0.4999 even though 0.4999 has more digits.
Always line up the decimal points before comparing digits.
Adding zeros to the right of a decimal doesn't change its value.
The first place where digits differ determines which number is larger.
Compare decimals by aligning their decimal points and comparing digit by digit from left to right. Start with the whole number part, then tenths, hundredths, and so on. The first position where digits differ determines which is smaller.
0.5 is bigger. When you align them (0.50 and 0.05), you can see that 0.5 has 5 tenths while 0.05 has only 5 hundredths. Think of it as 50 cents versus 5 cents.
Yes! Adding zeros to the right end of a decimal doesn't change its value. Just like $3.14 is the same as $3.1400. The zeros are placeholders that don't affect the value.
Add a decimal point and zeros to whole numbers. For example, to compare 5 and 4.9, think of 5 as 5.0. Now compare: 5.0 > 4.9 because 5 > 4 in the ones place.
If the whole numbers are equal, move to the tenths place. If those are equal, move to hundredths, and so on. For example, 3.456 > 3.445 because after the equal 3 and equal 4 in tenths, 5 > 4 in hundredths.
Negative decimals work opposite to positive ones. The number closest to zero is largest. For example: -0.5 > -0.8 because -0.5 is closer to zero. Think of it on a number line moving left.