Compare and Order Fractions and Decimals 2012-2013

Symbols of Equality and Inequality “Greater than” > “Less than” < “Equal to” = “Greater than or Equal to”≥ “Less than or Equal to” ≤

Equivalent Decimals Did you know…? We can add zeros to the end of any decimal without changing its value. We can use this to create EQUIVALENT DECIMALS. Ex. 0.2 = 0.20 = 0.200 = 0.2000… We can change a decimal from tenths, to hundredths, to thousandths and so on!

Equivalent Decimals We can remove zeros at the end of decimals too! Ex. 0.8000 = 0. 800 = 0.80 = 0.8 We just went from ten thousandths to tenths without changing the value!

Comparing Decimals This trick is very useful when comparing decimals! It is easier to compare them when they are in the same format. Apples to apples instead of apples to oranges. Place value charts can help us see this.

Now, go from left to right and Comparing Decimals Compare 0.347 to 0.5 Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones Tenths Hundredths Thousandths Ten Thousandths 0 3 4 7 0 5 0 0 Now, go from left to right and compare the numbers.

Ordering Decimals We can use this comparison technique to arrange decimals in order from least to greatest or greatest to least! Ex. Put these numbers in order from greatest to least. 0. 234, 0.009, 0. 0834

Comparing Fractions to Decimals In order to compare and order lists of numbers that contain fractions and decimals we must convert some of them to get them into the same format Comparing cats to cats is easier than comparing cats to fish!

Two Methods: 1. Change everything into fractions. use our conversion methods to convert all decimals into fractions Reduce the fractions Compare using LCD or draw pictures. 2. Change everything into decimals. Use our conversion methods to convert all fractions into decimals. Compare using place value chart or mentally.

Practice Are the following statements true? 0.436 > 0.099 3/4 < 5/6 2/5 > 0.13 Write in order from least to greatest. 1/2 , 2/9, 0.46 , 2.5

Negative Numbers Negative numbers are compared based on how far to the RIGHT they are. Ex. -1 > -2 (-1 is farther right than -2) Ex. -9 < 3 ( 3 is farther right than -9) Numbers get larger as we go to the right.

Examples Are the following statements true? -12 > 10 15 > -15 10 < -22 -5 < -3 Put in order from least to greatest. -12, 3.2, ¼ , -9, 4