Transcript Slide 1

1. Place Value
• Powers of 10.
• Can help us represent decimals as fractions:
0.2, 0.45, 0.20, 4.6, etc.
Decimals
• Most decimal numbers are rational numbers:
but some are not.
• A decimal is a rational number if it can be written
as a fraction. So, those are decimals that either
terminate (end) or repeat.
• Repeating decimals: 7.6666…; 0.727272…
• Terminating decimals: 4.8; 9.00001; 0.75
• A decimal like 3.5655655565555655556…
is not rational because although there is a
pattern, it does not repeat. It is irrational
• Compare this to
3.556556556556556556…
It is rational because 556 repeats. It is rational.
When decimals are equal
•
•
•
•
•
•
3.56 = 3.56000000
But, 3.056 ≠ 3.560.
To see why, examine the place values.
3.056 = 3 + 0 • .1 + 5 • .01 + 6 • .001
3.560 = 3 + 5 • .1 + 6 • .01 + 0 • .001
Think of units, rods, flats, and cubes.
Ways to compare decimals
• Write them as fractions and compare the
fractions as we did in the last section.
• Use base-10 blocks.
• Write them on a number line.
• Line up the place values.
Rounding
• 3.784: round this to the nearest
hundredth.
• Well, 3.784 is between 3.78 and 3.79. On
the number line, which one is 3.784 closer
to?
• 3.785 is half way in between.
3.78
3.785
3.79
Adding and Subtracting
Decimals
• Same idea as with fractions: the
denominator (place values) must be
common.
• So, 3.46 + 2.09 is really like
3 + 2 ones +
4 + 0 tenths +
6 + 9 hundredths = 5.55
Multiplying Decimals
• Easiest to see with the area model.
• 2.1 • 1.3
1
1
+
.3
+
1
+ .1
3. When decimals are equal
•
•
•
•
•
•
3.56 = 3.56000000
But, 3.056 ≠ 3.560.
To see why, examine the place values.
3.056 = 3 + 0 • .1 + 5 • .01 + 6 • .001
3.560 = 3 + 5 • .1 + 6 • .01 + 0 • .001
Think of units, rods, flats, and cubes-how
could we use them here?
4, Ways to compare decimals
• Write them as fractions and compare the
fractions as we did in the last section.
• Use base-10 blocks.
• Write them on a number line.
• Line up the place values.
5. Rounding
• 3.784: round this to the nearest
hundredth.
• Well, 3.784 is between 3.78 and 3.79. On
the number line, which one is 3.784 closer
to?
• 3.785 is half way in between.
3.78
3.785
3.79
6. Adding and Subtracting
Decimals
• Same idea as with fractions: the
denominator (place values) must be
common.
• So, 3.46 + 2.09 is really like
3 + 2 ones +
4 + 0 tenths +
6 + 9 hundredths = 5.55
7. Multiplying Decimals
• Easiest to see with the area model.
• 2.1 • 1.3
1
1
+
.3
+
1
+ .1
4, Ways to compare decimals
• Write them as fractions and compare the
fractions as we did in the last section.
• Use base-10 blocks.
• Write them on a number line.
• Line up the place values.
5. Rounding
• 3.784: round this to the nearest
hundredth.
• Well, 3.784 is between 3.78 and 3.79. On
the number line, which one is 3.784 closer
to?
• 3.785 is half way in between.
3.78
3.785
3.79
6. Adding and Subtracting
Decimals
• Same idea as with fractions: the
denominator (place values) must be
common.
• So, 3.46 + 2.09 is really like
3 + 2 ones +
4 + 0 tenths +
6 + 9 hundredths = 5.55
7. Multiplying Decimals
• Easiest to see with the area model.
• 2.1 • 1.3
1
1
+
.3
+
1
+ .1