How do you determine whether one decimal is larger than another for example 0.3 and 0.06?

Answer 1

There are at least two ways to compare decimal numbers.

1. Remember that a decimal is the same as a fraction with a power of 10 as its denominator. The number of zeros is the same as the number of places in the decimal, so

• 0.3 = 3/10
• 0.06 = 6/100

The common denominator for both is 100, so converting 3/10 to hundredths gives 30/100, which is greater than 6/100. Going back to decimal form, 0.3 > 0.06

2. Remember that putting zeros to the right of the last digit in a decimal doesn't change its value, the same way zeros to the left of a whole number don't change it (0005 = 005 = 05 = 5).

Put extra zeros to the right of the shorter decimal until it has as many places as the longer decimal. Next, ignore the decimal point. The number that's larger corresponds to the larger decimal.

In this case 0.3 has one digit to the right of the decimal point and 0.06 has two. Put an extra zero to the right of 0.3 to get 0.30 so the numbers are now 0.30 and 0.06. If you ignore the decimal points the numbers are 30 and 6; 30 > 6. The decimals are in the same order: 0.3 > 0.06

Both methods are actually the same! The difference is that the second method doesn't explain as much (not good if you have to show your work!) but after you practice it a few times it's a LOT faster.

- A harder one -

Put the following decimals in order from smallest to largest: a = 0.47, b = 2.1, c = 0.0029

You can do this quickly with Method 2.

• "a" has 2 digits to the right of the decimal point, "b" has 1, and "c" has 4.
• You need to add zeros so a and b also have 4 digits to the right: 0.4700, 2.1000, and 0.0029.
• Ignore the decimal points to get 4700, 21000, and 29. In order, 29 < 4700 < 21000 so the decimal order is 0.0029 < 0.47 < 2.1