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Decimal Fractions Guide: Place Value & Operations

This document provides information and examples about decimal fractions, including place value, addition, subtraction, multiplication, and division of decimal numbers. It explains that the decimal point must line up when adding or subtracting decimals. For multiplication, the decimal point stays in the same place. For division, you may need to move the decimal point by multiplying the dividend and divisor by powers of ten so no decimal remains in the divisor. Exponents with decimals are calculated by counting decimal places and square and cube roots follow similar rules. The document concludes with an activity of calculating various decimal fraction operations.

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MJ Dreyer
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85 views4 pages

Decimal Fractions Guide: Place Value & Operations

This document provides information and examples about decimal fractions, including place value, addition, subtraction, multiplication, and division of decimal numbers. It explains that the decimal point must line up when adding or subtracting decimals. For multiplication, the decimal point stays in the same place. For division, you may need to move the decimal point by multiplying the dividend and divisor by powers of ten so no decimal remains in the divisor. Exponents with decimals are calculated by counting decimal places and square and cube roots follow similar rules. The document concludes with an activity of calculating various decimal fraction operations.

Uploaded by

MJ Dreyer
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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Intervention 5

Decimal fractions –
The place value table:
Eg. 4218,375
Thousand Hundreds Tens Unit , Tenths Hundredths thousandths
s s
(Th) (H) (T) (U) , (t) (h) (th)
1
1 1
1000 100 10 1 , 1000
10 100
4 2 1 8 , 3 7 5
Find the place value and value of the digits 4 and 7 in the number 4218,375.
Solution:
The place value of 4 is 1000. The value is 4 x 1000 = 4000
1 7
The place value of 7 is hundredths ( ). The value is .
100 100

Adding and subtracting with decimal fractions:


The GOLDEN rule when adding and subtracting with decimal fractions is to ALWAYS
keep the comma right underneath each other. The comma can never be moved.
Step 1 – Write the numbers underneath each other with the comma under each other.
4 8 , 6 57
1 5 ,6 98 Remember when the
numbers don’t line-up
you add zero’s.
Step 2 – Write your operation +/-
4 8 , 6 57
+ 1 5 ,6 98

Step 3 – Start adding/subtracting the numbers that are in the same column, remember
carry over when a number exceeds 10.
1 1 1 1
4 8 ,6 5 7
+ 1 5 ,6 98
6 4 , 35 5

Subtracting works the same as the adding, you must just remember when you cannot
subtract go borrow at the next number.

Multiplication with decimal fractions:


When multiplying decimal fractions you use the same calculations as a normal
multiplication sum, but you make sure that the comma stays on the same place.

When multiplying with double digits remember to multiply each number with all the
numbers on top, then kill the number and give it a grave, repeat with the next number.
1. Place your numbers one on top of the other.
2. Multiply the bottom number by the number directly above it.
Record the unit in the answer box and carry the tens.
,
3. Repeat with the next number along and then the next.
4. Remember to add in the carried tens each time.
5. Add the comma in the correct place. ,
Division with decimal fractions:
The GOLDEN rule when dividing with decimal fractions: You never want to divide with a
decimal on the right hand side, thus you have to times with 10 , 100 , 1 000 or 10 000.

REMEMBER what you do on the one side, you have to do on the other side.

5,76 ÷ 0,3 x 10
= 57 , 6 ÷ 3

19,2

√3 5 7 ,6 Always keep the


- 3 comma where it is.

27
- 27
6
- 6

Exponents, square and cube roots:

Exponents –
Count all the spaces after the
(0.3)3 comma and that is then how
= 0,3 x 0,3 x 0,3 much spaces after the comma
your answer must be. After that
= 0,0 2 7 simply times the numbers
together

Square or cube roots - Count all the spaces after the


comma and then you know how
√ 0.008 = 0,2 x 0,2 x 0,2
3
many spaces was there in the
answer and then find the cube
root of the number.
= 0,2
Activity – Decimal fractions

Calculate the following.

a) f) k)

b) g) l)

c) h) m)

d) i) n)

e) j) o)

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