Comparing and ordering decimals and fractions

In this lesson, we will learn:

• How to compare decimals with decimals as well as fractions with fractions
• How to compare decimals with fractions using a number line or by converting into the same format
• How to order 3 or more decimals and fractions

Notes:

• When you compare two numbers, you always start with the biggest place value (most left) and then keep moving to the right (smaller place values) until you see a difference (the digits are different numbers).
• You compare numbers the same way for both whole numbers and decimals.
• For the numbers in each place value, 0 is the smallest and 9 is the biggest.
• Once you have found a difference for a place value, it does not matter what numbers are in the places further on the right (smaller places)
• The biggest place value (most left) that is different for the two numbers is what matters.


• Whenever you compare two numbers you need them to be in the same format; you will want to compare decimal vs. decimal (with same amount of place values) or fraction vs. fraction.
• To compare fractions with fractions
• Convert decimal numbers into fractions (have all fractions)
• Convert fractions into equivalent fractions with the same denominator
• Then, compare the numerators
• Ex. for $\frac{3}{10}$ vs. $\frac{20}{100}$ , you can either consider: $\frac{30}{100}$ vs. $\frac{20}{100}$ or $\frac{3}{10}$ vs. $\frac{2}{10}$
• To compare decimals with decimals
• Convert fractions into decimals (have all decimal numbers)
• If youre having trouble comparing decimals of different lengths, make all the numbers have the same number of decimal places by add trailing zeroes (add zeroes to the right)
• Then, compare the decimals


• Seeing where common fractions and decimals are placed on a number line can help you to understand ordering decimals in fractions:
• First, we can divide a number line into halves:

• Then, we can split each half into halves, making them quarters:

• We can also split a number line into tenths (ten pieces):

• We can further split number lines into hundredths by splitting each tenth into ten more pieces:

• To order a list of decimals and/or fractions, you must first convert them into the same format so that you can compare them. Then, follow the instructions of ordering either from:
• Least to greatest (increasing; smallest to biggest) or
• Greatest to least (decreasing; biggest to smallest)
• Review these symbols for comparing and ordering numbers:
• < less than
• > greater than
• = equal to