# Problems Working in Denary number base

• Jun 19th 2006, 08:45 AM
technics
Problems Working in Denary number base
I am doing an adult support course (for maths) and one the questions which I am struggling with (and have a deadline for tommorow) is

"Give two relevant examples of difficulties learners may face when attempting calculations in denary and the use of place value in denary."

can someone please give me fairly details examples for the above question.

much appreciated
• Jun 19th 2006, 09:24 AM
kbryant05
1 type of difficulty
(Denary)The decimal system name should not be used because of confusion that this could be thought as introducing the decimal point and money systems.
• Jun 19th 2006, 09:38 AM
technics
specific examples would be real helpful as my teacher wants examples e.g. in subtraction, division etc etc
• Jun 19th 2006, 12:15 PM
Soroban
Hello, technics!

Quote:

Give two relevant examples of difficulties learners may face when attempting calculations in denary
and the use of place value in denary.
Assuming we are involved in Arithmetic (and calculators are not used),
. . there are difficulties in almost every operation.

When adding (or subtracting) decimals, the decimal points must be aligned.

While previous (whole number) problems are always right-justified,
. . this is not true with numbers containing decimals.

Example: $\displaystyle 7.5 + 1.32 + 9 + 0.004$
Code:

The problem is NOT set up like this:           7.5         1.3 2             9       0.0 0 4       ------- Instead, it must be set up like this       7.5       1.3 2       9.       0.0 0 4       ------- Often, the "gaps" are filled with zeros.       7.5 0 0       1.3 2 0       9.0 0 0       0.0 0 4       ------- Then we can add and get: 17.824
When multiplying, the decimal points are not aligned.
But the decimal point in the product must be carefully placed.

Example: $\displaystyle 1.9 \times 2.47$
Code:

The problem is set up like this:         2.4 7           1.9       ------- Multiply "as usual":         2.4 7           1.9       -------       2 2 2 3       2 4 7       -------       4 6 9 3
Now the decimal point must be placed in the product.

The first number has two decimal places (counting from the right).
The second number had one decimal place.
. . We want the sum: $\displaystyle 2 + 1 \,= \,3$ decimal places.
Hence, the answer will have three decimal places: $\displaystyle 4.693$

There is an intuitive way to place the decimal point.

The product has $\displaystyle 4693$.
The answer could be: $\displaystyle 46930,\;4693,\;469.3,\;46.93,\;4.693,\;0.4693,\;$ etc.

Estimate the size of the answer.
2.47 is very close to 2.5 . . . and 1.9 is very close to 2.
Our problem is roughly: $\displaystyle 2.5 \times 2 \,=\,5$

The only choice which approximates 5 is: $\displaystyle 4.693$

I hope this is the type of stuff you were asking for.
If not, please clarify . . .
• Jun 19th 2006, 12:41 PM
technics
Thank you very much sir!