Study Guide for Chapter 3 Decimal TEST
Adding & Subtracting Decimals (p. 178)
Find the sum of 3.25 and 12.6.
Estimate 3.25 + 12.6 ≈ 3 + 13 or 16.
3.25
Line up the decimal points. Annex a zero so that both numbers have the same
+ 12.60
number of decimal places.
3.25
+ 12.60
15.85
Add as you would add whole numbers. Place the decimal point.
The sum is 15.85.
Example 2
Find the difference of 26.82 and 12.15.
Estimate 26.82 – 12.15 ≈ 27 – 12 or 15.
26.82
Line up the decimal points.
̶ 12.15
26.82
̶ 12.15
14.67
Subtract as with whole numbers.
The difference is 14.67.
Multiplying Decimals (p.194)
Use estimation as a strategy to check
the reasonableness of your answer.
Round 6.25 to 6.
6.25 × 5 → 6 × 5 or 30
12
6.25
× 5
31.25
Since the estimate is 30,
place the decimal point
after 31.
Multiply a Decimal by a Decimal (p. 202)
Count decimal places.
STEP 1: Multiply
6.25
There are two places to the right of
× 5
the decimal point.
31.25
Count the same number of decimal
places from right to left.
1). multiply the numbers as if you were multiplying all whole numbers.
2). find the sum of the number of decimal places in each factor.
3).The product has the same number of decimal places.
Example 1
Find 5.2 × 6.13.
Estimate: 5 × 6 or 30
5.2
× 6.13
156
52
+312
31.876
one decimal place
two decimal places
three decimal places
The product is 31.876. Compared to the estimate, the product is reasonable.
Example 2
Find 2.3 × 0.02.
Estimate: 2 × 0.02 or 0.04
2.3
× 0.02
0.046
one decimal place
two decimal places
Annex a zero to make three decimal places.
The product is 0.046. Compared to the estimate, the product is reasonable.
Dividing Decimals by a Whole Numbers (p.232)
When you divide a decimal by a whole number place the decimal point in the quotient above the decimal point in the
dividend. Then divide as you do with whole numbers.
Ex.
Find 8.58 ÷ 12.
Estimate: 10 ÷ 10 = 1
0.715
Place the decimal point.
12) 8.580
–84
18
Annex a zero to continue dividing.
–12
60
–60
0
8.58 ÷ 12 = 0.715 Compared with the estimate, the quotient is reasonable
Dividing Decimals by Decimals (p. 240)
When you divide a decimal by a decimal multiply both the divisor (turn the divisor into a whole number)
and the dividend by the same power of ten.
Then divide as with whole numbers.
Find 10.14 ÷ 5.2.
Estimate: 10 ÷ 5 = 2
Multiply by 10 to make a whole
number.
5.2)10.14
Multiply by the same
number, 10.
__1.95
52)101.40
–52
494
– 468
260
– 260
0
10.14 divided by 5.2 is 1.95.
Place the decimal point.
Divide as with whole numbers.
Annex a zero to continue.
Compare the quotient with the estimate
Example 2
Find 4.09 ÷ 0.02.
0.02) 4.09
Multiply each by 100.
4.09 divided by 0.02 is 204.5.
Check
204.5 × 0.02 = 4.09 
204.5
2)409.0
–4
00
–0
09
–8
10
–10
0
Place the decimal point.
Divide.
Write a zero in the dividend
and continue to divide.