# Comparing and ordering decimals and fractions

### Comparing and ordering decimals and fractions

#### Lessons

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 you’re 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
• Introduction
Introduction to comparing and ordering decimals and fractions:
a)
How do you compare two numbers?

b)
How do you compare decimals and fractions?
1. Why is 8.97 more than 9.795?
2. Why do you need to be in the "same format"?

c)
How to you place common fractions and decimals onto a number line?

d)
How do you order a list of 3 or more decimals and fractions?

• 1.
Comparing decimals up to thousandths
Compare decimal vs. decimal and circle the bigger value.
a)
0.164 and 0.162

b)
0.36 and 0.6

c)
.605 and 0.6

• 2.
Comparing the values of decimals with fractions
Compare decimal vs. fraction and circle the smaller value. (Or, circle both if they are equal and have the same value)
a)
0.5 and $\frac{1}{2}$

b)
0.8 and $\frac{3}{4}$

c)
$\frac{9}{25}$ and 0.34

d)
0.3 and $\frac{2}{5}$

e)
$\frac{7}{10}$ and 0.07

• 3.
Comparing and ordering decimals and decimal fractions
Change each value into all the same form and then write in order from least to greatest:
a)
Change all the following into decimals:
1. 2.19, 2$\frac{48}{100}$, 2$\frac{39}{100}$
2. $\frac{8}{10}$, $\frac{25}{100}$, 0.31
3. 1$\frac{666}{1000}$, 1$\frac{3}{5}$, 1.66

b)
Change all the following into decimal fractions
1. 0.493, 0.48, 0.479
2. 3.7, 1.65, 2.82
3. 0.46, 0.7, 0.3

• 4.
Comparing and ordering decimals and non-decimal fractions
Write the decimals/fractions in order from greatest to least*
a)
0.799, $\frac{8}{10}$, $\frac{3}{4}$

b)
$\frac{2}{5}$, $\frac{60}{100}$, $\frac{1}{2}$, 0.582

c)
$\frac{1}{25}$, $\frac{4}{1000}$, $\frac{11}{25}$, 0.444, $\frac{4}{10}$

• 5.
Word problem for comparing decimals and fractions
Ms. Johnson's science class is having a crystal growing competition. They are measuring the results by how heavy each student's crystal weighs. Who came in 1st, 2nd, and 3rd place?
 Student Name Crystal Weight James 70$\frac{11}{25}$g Lucas 73$\frac{67}{100}$g Emma 75.492 g Charlotte 70$\frac{1}{2}$g Ava $\frac{7891}{100}$g

• 6.
Word problem for comparing decimals and expanded form
Use the following words below each question; each set of words can make up a written form for several different decimal numbers.
a)
Rearrange the words below to create the largest number possible. Also, write the standard form of this number.

"hundredths, tenths, thousandths, four, eight, seven, nine, and"

b)
Rearrange the words below to create the largest number possible. Also, write the standard form of this number.

"thousand, thousandths, and, thirty-two, fifty-six"