Section 7.1 - Decimals
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1
2Chapter 7. Section 1
Page 1
Section 7.1 – Decimals
Homework (page 271) problems 1-9, 11-13
• Recall that 321 = 300 + 20 + 1 =
×
+
×
+ ×
2
1
0
3 10
20 10
1 10
is expanded form
• We have seen the exponents of 10 go from the ones place (10
0
3
) to the thousands place (10
) and even
further. Now we will extend this idea to negative powers of 10
1
1
5
• What does 10
×
−
= ×
=
–1
1
really mean? It is
. So if we have
5 10
5
10
10
10
• Now we can include fractional values!
Form of the Decimal:
• Recall that the decimal point is used for any values that are less than 1, it is our way of separating the
powers of 10 from the positive (0, 1, 2, 3 etc) to the negative ( –1, –2, –3, etc)
• Example
×
+ ×
+ ×
+ ×
−
+ ×
−
+ ×
−
2
1
0
1
2
3
123.567 =
1 10
2 10
3 10
5 10
6 10
7 10
• In the above example, the 5 is in the tenths place, the 6 is in the hundredths place, and the 7 is in the
thousandths place
Converting:
• Converting fractions to decimals uses our knowledge of fractions as division
0.5
5
•
=
=
10 5 10 5.0
10
• In fact, if 10 is the divisor (the denominator) then all we have to do is move the decimal place to the
left the same number of times as we have 0s
5
•
has 1 zero on the bottom, so we move the decimal place (5.0) to the left one time (0.5)
10
6
• Example. Convert
to decimal form.
100
Move the decimal point 2 places to the left
0.06
• Converting decimals to fractions is the reverse process, where you write the entire decimal value
divided by a power of 10
What power of 10 (how many zeros do you need)? The same as how many places you have to move
the decimal to get a whole number
• Example. Convert 0.45 into a fraction
45
=
0.45
(NOTE: you have to move the decimal 2 places to the right, so you need 2 zeros)
100
Exercises:
3
2
6
1
1
1
• Example, page 273 number 1c. Write
+
+
in decimal form
5
2
10
10
10
3
2
6
1
1
1
5
2
1
+
+
=
+
+
=
+
+
=
5
2
0.005 0.02 0.000001 0.025001
10
10
10
1000 100 1000000
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